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Modeling of Nitramine Propellant Combustion and Ignition
P.A. Politzer and J.S. Murray (Editors) Energetic Materials, Part 2: Detonation, Combustion Theoretical and Computational Chemistry, Vol. 13 9 2003 Elsevier B.V. All rights reserved.
Chapter 9
Modeling of Nitramine Propellant Combustion and Ignition Eun. S. Kim, Rongjie Yang, and Vigor Yang* *Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 104 Research Building East, University Park, PA 16802, United States of America NOMENCLATURE A A/ A sp
8j C, d,i
cross-sectional area of propellant sample pre-exponential factor of rate constant ofjth reaction specific surface area temperature exponent in rate constant of jth reaction molar concentration of ith species rate of change in molar concentration of ith species by jth reaction
Cpi
constant-pressure heat capacity of ith species
Di Dr, Ej e
effective mass-diffusion coefficient of ith species thermal diffusion ratio of ith species
A
Hf,,~
/-/sub nv
h
h, h}, k~
activation energy ofjth reaction internal energy fraction of laser energy absorbed by gas phase molar heat of fusion molar heat of sublimation molar heat of evaporation enthalpy enthalpy of ith species heat of formation of ith species at standard condition rate constant ofjth reaction
Corresponding Author. Email: [email protected]
295
296 j~PP
N
NR P P v ,eq
(2L "m
Q~d
R. s
T t u Vcof
v~ fv i fvRj
Xi x
mass flux total number of species total number of reactions pressure equilibrium vapor pressure of RDX external laser heat flux volumetric absorption of laser energy universal gas constant sticking coefficient temperature time bulk velocity correction velocity diffusion velocity of ith species molecular weight of ith species mass production rate of ith species mass production rate ofjth reaction mole fraction of ith species spatial coordinate mass fraction of ith species
Greek Symbols
P
/q p 2 &
absorption coefficient absorption cross section of ith species void fraction density thermal conductivity molar production rate
Subscripts 0+
0bw c
fw g id ini I
gas-phase side of propellant surface subsurface side of propellant surface backward reaction condensed phase forward reaction gas phase ignition delay initial condition liquid phase
297 l ---)g m net S
sur t v
from liquid to gas melting net value of evaporation rate minus condensation rate solid phase surface mass-averaged quantity in two-phase region vapor
1. INTRODUCTION Nitramines, including cyclotrimethylenetrinitramine (RDX) and cyclotetramethylenetetranitramine (HMX), are important oxidizer ingredients for solid propellants. These compounds are highly energetic and produce high impetus and specific impulse for gun and rocket propulsion applications. In comparison with ammonium perchlorate (AP), nitramines produce little smoke, toxicity, and corrosion. In order to meet the rising demand for various stringent performance and environmental requirements, the development of advanced energetic materials continues to be of strong interest to the solid-propellant community. Recently, attention has also been given to nitramine compounds with azide-containing energetic binder ingredients, such as glycidyl azide polymer (GAP), 3,3-bis(azidomethly)oxetane (BAMO), and 3-azidomethyl-3methyloxetane (AMMO), due to the unique characters of azide polymers. These highly energetic polymers have positive heats of formation but produce relatively low-temperature flames. Experimental and theoretical investigations of the complex processes involved in the combustion and ignition of nitramine monopropellants as well as nitramine/azide propellants have been a subject of extensive research. In the past decade, a great deal of experimental diagnostic and analytical modeling efforts have been applied to obtain more accurate and reliable data for the thermal decomposition, thermophysical properties, and flame structures of these propellants [1-24]. Significant advancements have been made in the modeling of combustion and ignition of nitramine and nitramine/GAP propellants [25-41]. The work involved the treatment of self-sustained and laser-assisted combustion [25-39], as well as ignition transients [39,40], with detailed chemical kinetics and variable thermophysical properties. The results have provided direct insight into the underlying mechanisms dictating the entire combustion and ignition processes. The effects of propellant compositions and ambient conditions on burning characteristics and combustion wave structures were examined in detail. This chapter is organized as follows. A short summary of various modeling efforts conducted in the past on nitramine and nitramine-composite propellant
298 combustion and ignition is first given. The state-of-the-art approaches recently developed in this subject area are then described along with a brief discussion of the numerical techniques. Finally, results of these modeling studies are summarized.
1.1.
Modeling
Development
of
Steady-State
Combustion
of
Nitramine
Propellants
The molecular structures of RDX, HMX, and GAP are "shown in Fig. 1. Most of early theoretical analyses of steady-state combustion of nitramine propellants were based on global reaction schemes for gas-phase processes [42]. The first comprehensive model of RDX combustion, accommodating 23 species and 49 reactions in the gas phase, was initiated by Ermolin et al. [43]. The propellant surface conditions, however, were treated as input parameters in order to match experimentally measured species-concentration profiles. A substantial improvement was made by Melius [25] to relax this constraint. His formulation simultaneously took into account the thermal decomposition of RDX and the ensuing chemical reactions to an extent that the key heat-release mechanisms could be identified. Yetter et al. [26] refined Melius' model to include the sub-models of reactions among the major intermediate products such as CH20, NO2, N20, H2, HCN, and NO, but a significant amount of uncertainties still existed about the pathways of the reduction and associated rates of large fragments departing from the burning surface of these cyclic nitramines. By considering global reactions, Margolis, Williams, Li, and coworkers [27-29] developed an analytical approach, which included the presence of gas bubbles and liquid droplets in the two-phase region near the propellant surface by means of methods of matched asymptotic expansion. The model, however, provided limited information concerning the chemical processes. Prasad et al. also studied self-sustained and laser-assisted
O,N /N\
O,N.. H-. ~NO~ C.N" N, c.2
O2N
/N C
CH2
_ /N\No-,
O2N/
N \ c~N\No2
H,
H2
RDX
HMX
1 ' H ~ O--CH--CH2 ;
,
,
OH
{
{ H_,CN--N2 ~ ~ n
GAP
Fig. 1 Molecular structures of RDX, HMX, and GAP.
299 combustion of RDX and HMX [30,31]. Their model differed from the ones described in Refs. 25-29 in that bubble formation within the liquid layer was neglected. In general, these models of RDX and HMX combustion predicted burning rate, surface temperature, and melt-layer thickness reasonably accurately, although some disagreements with experimental data in the nearsurface species profiles and the temperature sensitivity of propellant burning rate were noted. Recognizing the important role of the condensed phase, Liau and Yang developed a detailed model of RDX combustion accounting for the foam layer, which is the region between the gas and solid phases [33,34]. Such a foam layer consisted of two phases: liquefied RDX and bubbles containing gaseous RDX and its decomposition products. Davidson and Beckstead [35] further studied the near-surface temperature distribution and pressure sensitivity of burning rate. The similar approach was later extended to study the combustion behavior of HMX [36]. Studies on the physical properties, sublimation, decomposition, ignition, and self-deflagration of nitramine propellants conducted prior to 1984 are summarized by Boggs [44] and Fifer [45], and the state of understanding of steady-state combustion of nitramine propellants up to 1990 is given by Alexander et al. [46]. A summary of the latest development is covered in a volume edited by Yang et al. [47].
1.2. Modeling Development of Ignition of Nitramine Propellants Ignition of solid propellants and explosives involves an array of intricate physiochemical processes under energetic stimuli, and has been a subject of extensive research since 1950. A comprehensive review of the early work was conducted by Price et al. in 1966 [48]. The experimental and theoretical literature pertaining to the ignition of solid propellants over the period of 1966 through 1980 was reviewed by Kulkarni et al. [49] and Hermance [50]. The state of understanding in Russia up to 1989 was presented by Vilyunov and Zarko [51], giving a detailed examination of the various ignition models and related experimental approaches. In 1998, a review of laser and radiative ignition of 24 solid energetic materials, with emphasis on work performed in the Former Soviet Union. was provided by Strakouskiy et al. [52]. Many theoretical ignition models have been developed to study the ignition of solid propellants and explosives, which can be broadly divided into four categories: solid-phase (or reactive solid), heterogeneous, gas-phase, and multiphase reaction models. The solid-phase reaction models [53-56] assume that exothermic reactions in the condensed phase are the dominant mechanism of ignition, while the effects of surface and gas-phase processes are secondary and can be neglected. Heterogeneous reaction models [57-65] assume that heterogeneous reactions at the propellant surface are responsible for ignition
300 due to the molecular diffusion of ambient oxidizer species to the propellant surface. The formulation takes into account the condensed-phase conservation equations of energy and species concentration along with interfacial boundary conditions. Unlike the previous two categories, the gas-phase reaction models [66-73] presume that exothermic gas-phase reactions and their heat feedback to the propellant surface are the primary mechanism of ignition. Conservation of energy and species concentration in the gas phase is of major concern, but the condensed-phase equations are also included for completeness. In spite of their contributions in correlating experimental data and providing qualitative understanding of ignition behavior, the solid-phase (or reactive solid), heterogeneous, and gas-phase reaction models [53-73] are semi-empirical in nature and do not provide predictive capability at scales sufficient to resolve the detailed ignition mechanisms and flame evolution. A prior understanding of the ignition process is usually required before modeling. This obstacle mainly results from the use of global kinetics schemes derived for steady-state combustion. Moreover, a simple pyrolysis law is often employed to describe the propellant gasification process in terms of propellant surface temperature along with prescribed condensed-phase heat release. Recently, Liau, Kim, and Yang developed a multi-phase reaction model by extending the steady-state model described in [33,34] to include the transient development in the entire combustion zone, including the solid-phase, nearsurface two-phase, and gas-phase regions [39,40]. The formulation accommodates detailed chemical kinetics and transport phenomena in the gasphase region, as well as thermal decomposition and subsequent reactions in the two-phase region. Thermodynamic phase transition and volumetric radiant energy absorption are also considered for a complete description. The model is capable of treating the entire ignition process from surface pyrolysis to steadystate combustion, with the instantaneous burning rate and surface conditions treated as part of the solution [39,40]. A summary of the theoretical formulation and results of this multi-phase model is given in the following sections of the current chapter.
1.3. Modeling Development of Combustion of Nitramine/GAP PseudoPropellants Most of the early work on GAP decomposition and combustion was based on global decomposition pathways [74]. The physiochemical processes involved in the combustion of a cured GAP strand is schematically illustrated in Fig. 2. The entire combustion-wave structure can be segmented into three regions: solid-phase, near-surface two phase, and gas-phase regimes. In the solid phase, the extent of chemical reactions is usually negligible due to the low temperature and short residence time. Thermal decomposition and ensued
301
reactions, as well as phase transition, take place in the foam layer, generating gas bubbles and forming a two-phase region. Rapid gasification occurs at the burning surface, and further decomposition and oxidation continue to take place and release a significant amount of energy in the near-surface region. The burning surface temperature is greater than 700 K. No visible flame is observed in the gas phase" instead, a large amount of fine powder is formed away from the burning surface and generates a cloud of intense smoke. The final flame temperature of GAP is around 1300-1500 K, which is significantly lower than those of nitramines (-- 3000 K).
:t Major Species: ~(~Invisible 1 1i N_,, HCN. CO. CH_,O, NH3. i/Flame l CH~CHO. CH_-CHCHNH. ~.. CH~CHNH. H-O, CHa. C-H~ j) 9 - -~ (Yellow Fine "~ L ~ 9 [Powder (Formed[ 9 . -~"-~.~in Gas P h a s e ) J : Decomposition. Evaporation, " [ and Gas_Phase Reactions (Bubble) 1" " ". " " . " 7",." - 1500 K
:d Phase T,- - 700-800 1050 K [2
Solid Phase ]
Fig. 2 C o m b u s t i o n - w a v e structure of GAP.
In recent years, Yang and coworkers [37-39] have established comprehensive numerical analyses of nitramine/GAP pseudo-propellant combustion to predict the propellant burning rate and detailed combustion wave structure over a broad range of pressure, laser intensity, and propellant composition. The steady-state model described in [33,34] was extended to include GAP binder in the nitramine combustion. The model takes into account various fundamental processes at scales sufficient to resolve the microscopic flame-zone physiochemistry. The thermochemical parameters of nitramine and GAP are deduced from existing experimental data. Four global decomposition reactions in the condensed phase as well as subsequent reactions are included. In the gas phase, a detailed chemical kinetics scheme involving 74 species and 532 reactions is employed to describe the heat-release mechanism. The key physiochemical processes dictating the propellant burning behavior and flame
302 structure were studied over a broad range of ambient pressure, preconditioned temperature, propellant composition, and impressed laser intensity. The model approaches and results for HMX/GAP [37,39] and RDX/GAP [38] combustion will be briefly discussed in the current chapter. 2. T H E O R E T I C A L F O R M U L A T I O N Three physical problems are considered in this chapter: 1) steady-state combustion of nitramine propellants; 2) laser-induced ignition of RDX monopropellant; and 3) steady-state combustion of nitramine/GAP pseudopropellants. During the past decade, Yang and co-workers [33,34,37-41] have developed a series of comprehensive numerical models for studying the key physiochemical processes involved in combustion and ignition of nitramine monopropellant and nitramine/GAP pseudo-propellants. These models accommodated detailed chemical kinetics and transport phenomena in the gas phase, as well as thermal decomposition and subsequent reactions in the condensed phase. The formation of gas bubbles in the molten surface layer due to molecular degradation and thermodynamic phase transition is also included to provide a complete description. The steady-state combustion models [33,34,37-39] are capable of resolving the combustion-wave structures in both the gas and condensed phases, with the instantaneous burning rate and surface temperature calculated as part of the solution. The analyses [33,34] were later extended to treat the entire ignition process from surface pyrolysis to steadystate combustion [39,40].
2.1. Steady-State Combustion of RDX Monopropellant Figure 3 shows the physical model of concern, a strand of RDX monopropellant burning in a stagnant environment with or without the assistance of external laser heat flux. To facilitate formulation, the entire combustion-wave structure is conveniently segmented into three regions: 1) solid phase; 2) near-surface two phase, and 3) gas phase. During burning, the propellant remains thermally stable in the solid phase until the temperature approaches the melting point at which thermodynamic phase transition occurs as shown in Fig. 4. Molecular degradation and evaporation of RDX then take place in the liquid layer, generating bubbles and forming a two-phase region. The propellant subsequently undergoes a sequence of rapid evaporation and decomposition in the near field immediately above the foam layer. Oxidation reactions continue to occur and to release an enormous amount of energy in the gas phase, with the final temperature reaching the adiabatic flame temperature. A detailed description of the theoretical model can be found in Refs. 33 and 34.
303 x gaseous f 38 spec=es flame / 158 or 178 reactions region (Metus, Yeller)
[ ,2 decoml:oSition pathways - I 1 gas-phase reaction ", o. ,%. o~_foam layer~ eva,oorationVcondensation t - L (mi,) pretmated region phase transition T
RDX deco.,m~sition HCN+HONO
3000K
pdmarlfflame~_ NO+CO+N2 seconda~fla_me~ N2+CO+H20
+CH20+N20
+H20+HCN
+CO2+H2
,etc.
,etc.
,etc.
Fig. 3 Strand of RDX burning in a stagnant environment.
gas phase
RDXvapor
Q
c:> o
o
foam layer
o o
o
o
solid phase
Fig. 4 Schematic diagram showing various regions in RDX combustion-wave structure.
2.2. Laser-Induced Ignition of RDX Monopropellant The physical problem of concern is the ignition of a strand of RDX monopropellant induced by a continuous and radially uniform CO2 laser. The physiochemical processes involved are schematically illustrated in Fig. 5. The propellant and the ambient gas are initially at room temperature. Once the laser is activated, volumetric absorption of laser energy in the solid phase takes place, as shown in Fig. 5a. In the gas phase, only certain gaseous species, such as vapor RDX, absorbs a noticeable amount of laser energy at the wavelength of 10.6 ~tm; thus, the gas-phase absorption is negligible during the inert heating period. When the solid reaches its melting temperature, the absorbed radiant energy can not further raise the temperature without first melting the solid. Since the radiant energy absorbed is insufficient for instantaneous melting of all of the solid in a short period, partial melting of the solid occurs, which leads to the formation of a mushy zone consisting of both solid and liquid (Fig 5b).
304 When a pure liquid layer is formed, the solid-liquid interface starts to move due to conductive and radiative heat transfer (Fig. 5c).
I Gas Ph~el
__T2 Ambient ~ Temperature Gas qt,l,.;___w.~t Profile -
-
- ----~-~----
-,"---"--
(a)
Solid
............
Tin,
x'--
l
Mushv
. - - - ~ --~, i ' ~ ' ~ -~ Liquid Ambient ~1~:~ ... Gas ,, - - - - ~ . . I re,it
~
Solid
(b)
t
T*..- Foam Zone - Ambient
Mushy - - zone
~
!! / < t,d
77., X-'---"l
'-Tmelt
TI t
'\ ~
Foam
Zone --~
- oo Mushy
i'-- Zohe
Pyrolyzed ~ ~qh Gas
(d)
~ ~ - - - ' - ~ - '
X "'--
~ T,.,
~_ Tnx:lt
,
-
t
~o
l
T':
\
'l
X'"J
._-2
T
~
~
Foam
Zone ---
t"-- Zone
k-Tmelt \, Foam . ~ Zone --~
u
Mushy
- ~
Mushy
~--Zone ~:l
Solid i t>tid
Fig. 5 Physiochemical processes involved in laser-induced ignition of RDX. In the liquid, thermal decomposition and subsequent reactions, as well as phase transition, take place, generating gas bubbles and forming a two-phase region. The propellant then undergoes a sequence of rapid evaporation at the surface (Fig. 5d). Ignition occurs if the heat flux is sufficiently large to initiate the subsequent self-accelerated exothermic reactions which result in substantial heat release (in the gas phase) and emission of light. A luminous flame is
305
produced, regresses toward the surface, and finally reaches a stationary position corresponding to its steady-state condition. A brief description of the theoretical model is given in the Section 2.4. with detailed information available in Refs. 39 and 40.
2.3. Steady-State Combustion of Nitramine/GAP Pseudo-Propellants Figure 6 shows schematically the physiochemical processes involved in the HMX/GAP pseudo-propellant combustion. A physical model for RDX/GAP pseudo-propellant combustion is available in Ref. 38. The entire combustionwave structure is segmented into three regions: solid phase, near-surface Tt - 2800 K
~Rapid Consumption of ~ L.. HCN and NO J
(MajorSpeciesinDarkZone: N.. H.O. NO. CO. HCN. H.CO. N,O. H.. CO. Td,,,.k ......
--
_~ ~econdary ] " ~ l a m e ZoneA
" ~ ,
Dark Zone
1250 K
., " o ~ (~AP Polymer'i (',... ") ('Decomposition, Evaporation, i~ - ~ " "[Residue ~] - x_A vnmary | [ and Gas-Phase Reactions (Bubble)[ ~ A o ~ 9 "x...Flame Zone fl " -~ ~ - ~ O ~ ' V " ,.~_.~ O__~, (HMXVapor ~,~n v ~ ~ ~L.V ' ~ , ~ b ~ d J l l V ~ q ~ . ' ~ l ~ /Liquid Interface)
(HMX Melt Front) ~
I. SolldPhase ~ HMX
GAP
Fig. 6 Combustion-wave structure of H M X / G A P pseudo-propellant at 1 atm.
two phase, and gas phase. In the solid-phase region. HMX powder and GAP are physically mixed. The former melts at 558 K with negligible chemical reactions taking place, due to the low temperature and short residence time. Thermal decomposition and phase change of HMX occurs in the liquid phase to form a foam layer. The propellant surface (x = 0) is defined herein as the interface between the foam layer and gas-phase region, at which rapid gasification of HMX prevails. Since the surface temperature of HMX/GAP pseudo-propellant (-700 K) is lower than that of pure GAP, GAP leaves the surface as aerosol surrounded with vapor HMX and its decomposed gaseous
306 products. In this region, GAP remains as a condensed species and continues to decompose. A significant amount of carbonaceous residue may be present on the surface during combustion. To facilitate analysis, the coordinate system is fixed at the propellant surface. A quasi one-dimensional model is formulated as a first approximation of the problem. Both the sub-surface and near-surface regions require a multi-phase treatment because of the presence of GAP and other condensed species in these zones. A detailed derivation of the theoretical model is available in Refs. 37 and 39. A similar model approach has been applied for studying RDX/GAP pseudo-propellant combustion [38].
2.4. Conservation Equations A brief summary of the theoretical formulation of physicochemical processes in various regions during the laser-induced RDX ignition process [40] is given below. The model for steady-state combustion can be treated as a limiting case by neglecting all the time-varying terms.
2.4.1 Gas-Phase Processes The formulation for the gas-phase region is based on the mass, energy, and species transport for a multi-component chemically reacting system of N species, and accommodates finite-rate chemical kinetics and variable thermophysical properties. If body force, viscous dissipation, and kinetic energy are ignored, the conservation equations for an isobaric flow can be written as follows. Mass a(pA) + - - (p,,A) = 0, ~t Ox
Species concentration 9A ~~J+Y,p u A OYi +~(9AViYi 0 )= A~'vi ot 0x 0x
(1)
(i = 1,2..... N),
(2)
Energy pcpA~)T~)(pA)+pucAi)T~__~._.(LAi)T~_i~I( ~t ~t P ~x = Oxk, Ox ) a
i)T + r PYiVict, i -~x
, i ] .+, ,AQrad.g (3)
where subscript i denotes the ith species. The specific enthalpy hi is defined by
hi = fir,t c1,,dT + hs,
(4)
Standard notations in thermodynamics and fluid mechanics are used in Eqs. (14). The mass diffusion velocity 5',- consists of contributions from both concentration (i.e., Fick's law) and temperature (i.e., Soret effect) gradients,
307 V,=-D, - -1 ~ X,
+ D
o,~
Dr - 1- ~~
--~'
(5)
+ V
X i T o~x
co,
where the correction velocity Vco, is employed to ensure that N
~ Y E =0
(6)
1=1
The ideal-gas law for a multicomponent system is derived to close the formulation. p = pR, T
•,__,wY
(7)
2.4.2 G a s - P h a s e C h e m i c a l K i n e t i c s
For a set of NR elementary reactions involving N species, the reaction equations can be written in the following general form: kfw I ,V
N
Zv;iM -~i
i = Zv~M,, k bw ! 7-i "= ,
j:
1,2 .....
g R
(8)
where v~ and v~ are the stoichiometric coefficients for the ith species appearing as a reactant in the jth forward and backward reactions, respectively, and M; is the chemical symbol for the ith species. The reaction-rate constant k, (either ke~, or kb,,.' ) is given empirically by the Arrhenius expression
k, = AjT 8 exp(-Ej / R.T)
(9)
The rate of change in molar concentration of the ith species by the jth reaction is N
= ( Tj
9
N
9
1-I c ?
FI c 2 )
i=i
i=i
(lO)
The net rate of mass production of the ith species ~i,i in Eq. (2) is then obtained by summing up the changes due to all reactions: NR
~, = w, ~ dT,j
(11)
j=!
It must be noted that the expression for chemical reaction rates, Eq. (10), is valid strictly for elementary reactions. If a global kinetics scheme is used, the exponents for molar concentrations may differ from their stoichiometric coefficients in order to match experimental data. The detailed reaction mechanism proposed by Yetter [26] and augmented by Lin and co-workers [4] is employed to treat the gas-phase chemical kinetics. The model is developed based on a hierarchical approach for collecting kinetic
308 data and the specific chemical sub-models that are required to form the gasphase combustion mechanism [26]. In particular, three kinetic sub-models of increasing complexity (N20 decomposition, H2/NO2 reaction, and CHa/N20 reaction) are established using the results from kinetics experiments over a broad range of temperature and pressure. When the initial decomposition steps of RDX proposed by Melius [25] are adopted, the overall scheme contains 38 species and 178 reactions. Here, the N-N bond cleavage is assumed to be the first step of the gas-phase decomposition process of RDX due to its weak bond energy of about 50 kcal/mol compared to - 60 kcal/mol for the C-N bond and -90 kcal/mol for the C-H bond. Li and Williams [29], however, indicated that the initial dominant decomposition pathway might be concerted symmetric triple fission to produce three H2CNNO2 fragments at high temperatures. At present, uncertainties still exist about the types of species formed and their associated rates, especially for regions in close proximity to the burning surface. More experimental investigation isneeded to clarify the initial decomposition steps of RDX. In the past. detailed kinetics models have been implemented to simulate self-sustained and laser-induced combustion of RDX under steadystate conditions [33,34]. Reasonably good agreement was obtained with experimental data in terms of propellant burning rate and flame structure. Three deficiencies, however, were observed: 1) insufficient quantities of N2 and NO2 in the first stage of flame, 2) abundance of CH20 at the end of the first stage, and 3) over-prediction of the ignition delay. Modifications were thus undertaken to circumvent these problems in three steps. First, a reaction allowing for the formation of N2 during the initial stage of reaction was added to the model. Second, the rate of thermal decomposition of H2CN was increased to allow for greater H-radical generation and subsequently for faster consumption of CHzO. Third, a reaction between HzCNNO2 and NO2 was added to enhance the ignition process. Recently, Lin and coworkers [4] revised the near-surface combustion mechanism by adding more reactions involved in the consumption of H2CNNO2, H2CNNO, HzCNO, H2CNOH, and H2CN. The kinetic rates of these added reactions were determined using high-level ab initio molecular orbital (MO) and statistical theory calculations [4]. The resulting kinetics scheme, containing 49 species and 250 reactions, can be found in Ref. 39.
2.4.3 Subsurface Two-Phase Processes The liquid and gas bubbles underneath the propellant surface are treated together and referred to as the subsurface two-phase region. The physiochemical processes in this region are extremely complicated, involving an array of intricacies such as thermal decomposition, evaporation, bubble formation, gas-phase reactions in bubbles, interfacial transport of mass and
309 energy between gas and condensed phases, etc. Taking full account of these processes is hardly practical, and many simplifications have been made to render the analysis manageable. A two-phase fluid dynamic model using a spatial averaging technique is employed to formulate the complicated phenomena in the two-phase region [33,34]. The mass diffusion velocities in the two-phase region V,:iand V,; are assumed to be relatively small compared to their convective counterparts in the gas phase, and are ignored to simplify numerical calculations. The conservation equations for both the liquid phase and gas bubbles can be combined into the following form: Mass .
O[(1-O)p,,,,
at
]
+op~
Ox
(12)
-0
Species concentration f o r liquid p h a s e
~)[(1- 0)Pt It, ] *. ~ [(! 0t
0x
(:)p, u t Yti l = ,vii
(i= 1.2..... N t )
(13)
Species concentration f o r gas p h a s e
at
= ,i:g i
F
(i=1,2
.....
Ng )
(14)
a x
Energy ,
a p, c l,., -~t + p'"'c p'' ~Ox -ax _
2, oT'
-~x;
V.
N ~.
Z hlj,i..O Z h, ,i,.
_
:=l
-
j=l
+ Z hgjI:~'i:t~g
(15)
j=l Nc
- ZhljYliWl~g
+Q~ad.l
j=l
where subscript t denotes the mass-averaged quantity in the two-phase region. The source terms, %. and ,~,,, represent the mass production rates of the ith species in the liquid phase and gas bubbles, respectively, and ~i:t_~g represents the mass conversion rate from liquid to gas.
2.4.4 Subsurface Chemical Kinetics a n d Phase Transition
The global decomposition model of RDX proposed by Brill et al. [12], derived from a well-calibrated temperature-jump/Fourier transform infrared (T-
310
jump/FTIR) spectroscopy experiment, is adopted here. includes two pathways as follows" RDX,:.
kl ) 3CH:O + 3N_,O
RDX ,
k: >3HCN + 3HONO
.
This mechanism (R1)
fast -> 3HCN + -3 NO + -3 NO, + -3 H ,O 2 2 2 -
(R2)
Reaction (R1) is an exothermic, low-temperature pathway, whereas reaction (R2) is an endothermic, high-temperature pathway. The reaction rates are obtained tu a model of the T-jump/FTIR experiment [15], which takes into account the heat transfer of the filament and sample. kl = 6"00•
-
36.0 kcal/mol) s_ I
(16)
RuT
~'VRi = ( I -- ~) )ptkl
(
k 2 = 1.60• 1.'t,'R2 --
-
( 1-
45.0 kcal/moi) R,,T
s
_i
(17)
)Ptk2
r
The two global decomposition reactions are nearly thermally neutral at temperatures around 600 K. Subsequent reactions among the products of (R1) and (R2) may occur and provide the energy to sustain pyrolysis. Brill [12] examined several plausible secondary reactions, such as CH20 + NO2, CH20 + N20, and HCN + NO2, and their corresponding reaction rates. Results indicated that the following reaction NO 2 + C H 2 0
(R3)
t~ ~ N O + C O + H _ , O
is probably the most important secondary reaction in the subsurface region. The reaction rate of (R3) has been determined from shock-tube experiments [16] and is given by (
k3 =8"02•
~R.~ =,~.~
-
13-7 kcal/mol) R,,T
P.~ YCH,o P vYNO~ WCH
_, O
cm3 mol-sec (18)
WNO-~ _
In addition to the thermal decomposition and its subsequent reactions (R1R3), thermodynamic phase transition from liquid to vapor RDX is considered to provide a complete description of the mass conversion process. RDX(,, r
RDX,,~,
(R4)
311 Based on gas-kinetic theory, the net evaporation rate is taken to be the difference between the evaporation and condensation rates [33] and is expressed as
rune t = S "~- //'IVRDX
R,,T
/p q_x ox/ p
Thus, the specific mass conversion rate due to evaporation becomes ~'R4 = Aspth2e,
(20)
The specific surface area A,p is a function of void fraction and number density of bubbles, and is derived as follows. Asp =(36mz)ll~O "-13, 0 < 1/2 or (36mz)J13(l-O) 21~, 0 > 1 / 2
(21)
where n is the number density of gas bubbles to be determined empirically [33]. 2.4.5 Solid-Phase Processes Since very little RDX decomposes in the solid phase, due to its low temperature conditions, only the energy conservation equation that includes both conductive and radiative heat transfer is required to model the solid-phase processes. The equation takes the form p, cp..~ --~t + p,u.~c,,.s --~-x= -~-x~ ' -~x + Qrad.,
(22)
where subscript s represents solid. The thermal properties of RDX were recently measured by Hanson-Parr and Parr [ 17]. Since the properties of liquid RDX, such as 21 and c r ~, are not available in the literature, the same values are used for both the liquid and solid RDX. The thermodynamic and transport properties of RDX used in this analysis are available in Ref. 39. 2.4.6 Radiative Heat Transfer The radiative heat transfer processes are complicated and difficult to model, usually including absorption, emission, and scattering of radiant energy in both the gas and condensed phases, as well as surface absorption, transmission, and reflection. In this work, the focus is on a CO2 laser with a wavelength of 10.6 l,tm. The following assumptions are made to render the analysis feasible. First, the CO2 laser is treated as collimated irradiation and locally one-dimensional. Second, reflection at the propellant surface is not considered, since the normal reflectivity of RDX with a refractive index of 1.49 at 10.6 g m was estimated to be only 0.047, using Fresnel's equation [ 18] Third, the levels of scattering by and emission from the gas-phase, two-phase, and solid-phase regions are
312 assumed to be relatively small compared to that of absorption. Finally, Beer's law is employed to determine the volumetric absorption in the solid- and twophase regions as follows. The absorption in the solid and subsurface two-phase regions (x < 0) is Qrad.,. =(1- f~, -Cts,~ )(l-O)fl,.e"-~'P,-~'Q(~e~
(c= liquid, solid)
(23)
where f, is the fraction of laser energy absorbed in the gas-phase region, ~ur the fraction of laser heat flux absorbed by the propellant surface, ,6'~ the absorption coefficient, and Qi~s~r the laser heat flux. The absorption coefficient of solid RDX for a CO2 laser at a wavelength of 10.6 ktm has been measured by Isbell and Brewster [18] to be 2800 cm -~. Since the absorption properties of many types of semi-transparent liquids are quite similar to those of solids [75], the absorption coefficients of solid and liquid RDX are assumed to be the same in this work. The fraction of laser energy absorbed in the gas-phase region fg is defined by the following equation:
fO_;a fg = 0..q___~ Q~'a~er
(24)
where 0,~.~ is the gas-phase absorption of laser energy, and can be estimated by examining the infrared (IR) transmittance data. The vapor RDX IR spectrums obtained using both confined rapid thermolysis (CRT)/FITR spectroscopy [13] and rapid-scanning FTIR spectroscopy [19] show strong, broad absorption bands of vapor RDX in a wavelength range of 4.7 to 13.3 ktm. The absorption characteristics of the gaseous decomposition products of RDX at 10.6 ~m can be readily studied from their corresponding individual IR spectra [76]. None of the major decomposition products exhibits a noticeable absorption at 10.6 ~m. It is clearly evident that of the species present, only vapor RDX absorbs a considerable amount of CO2 laser energy in the gas phase. Thus, volumetric absorption in the gas phase is given by "w
"a
Q~ad.,r = CRDXA,."CRDX.gQl~er
(25)
where CRDX is the molar concentration of vapor RDX, and Av Avogadro' constant. The absorption cross-section of vapor RDX, ~r is defined as rRox~ = ~~. WRDX
(26)
PRDX.,-A,.
Since the absorption properties of vapor RDX are not available in the literature, the absorption coefficient fl~ is used to estimate ~'RDx.s with the assumption that
313 the characteristics of vibration-rotational bands of vapor RDX at the wavelength of interest are similar to those of intermolecular vibration bands of condensed RDX [75]. An IR transmittance spectrum for solid RDX, obtained from the measurement of RDX powder pressed in a KBr matrix [20] shows a strong absorption band of solid RDX at 10.6 ~m, similar to the absorption characteristics of vapor RDX. At present, the use of the same absorption properties for both condensed and vapor RDX seems to be reasonable, due to the lack of measured data. Note that a parametric study has also been performed by varying the absorption coefficient of vapor RDX by 20 % in order investigate the effect-of absorption properties on the overall ignition process.
2.4.7 Boundary Conditions The physical processes in the gas-phase and subsurface regions must be matched at the interface by requiring continuities of mass and energy fluxes. This procedure eventually determines propellant surface conditions and burning rate as the eigenvalues of the problem. The interfacial boundary conditions are expressed as follows:
Mass (27)
(pu) o_ =[(I-~)p/u t +Op~ttg ]o-
Species concentration LO(tt + Vi )Yi ]o + =[(l-q~)PlUIYli + r
(28)
o-
Energy f2dT]
I2 dT]
H,,
(29)
where subscripts 0 § and 0 represent conditions at the interface on the gas-phase and subsurface sides, respectively. Note that Eq. (27) is essentially the summation of mass fluxes of all species governed by Eq. (28), and thus can not be independently used for determining the eigenvalues. An additional condition is required. Here, the thermodynamic phase transition from liquid to vapor RDX is assumed to prevail at the interface, o_,ivin,,
(P,",)o- = 'n,,~,
(30)
Equations (28-30), coupled with the assumptions that Tg = Tl and pg,g = p~ut in the condensed phase, are sufficient to solve the set of unknowns (ut, 7", O, Yi) at the propellant surface. The far-field conditions for the gas phase require the gradients of flow properties to be zero at x ~ oo.
314
O___pp= O t__jt= ~ Y. _- O T -- 0 a t x ~
~x
Ox
~x
oo
(31
)
bx
The condition at the cold boundary for the solid phase (x ~ _oo ) is T = Ti. i
(32)
at x - - ~ - o o
Finally, the conditions for the phase transition from solid to liquid at the melting point (T,,, = 478 K) are required. T , = T, = T,,,
and
(33)
k ~T.
=k ~,
p,n,.,(ax,,
)
,,
at x - x .... where subscripts x,,,+ and x,,, represent conditions at the interface on the two-phase and solid-phase sides, respectively. 3. N U M E R I C A L M E T H O D The theoretical formulation established in the preceding section requires a timeaccurate analysis. A dual-time-stepping numerical integration method is employed to circumvent the computational difficulties associated with the rapid transients during the ignition process. The scheme includes artificial time derivatives, so that the solution converged in pseudo-time corresponds to a time-accurate solution in physical time. The physical time step is chosen to be around one hundredth of the estimated ignition delay, or even less, to obtain reasonable temporal resolution. When marching from one physical time level to the next. all the conservation equations and associated boundary conditions are solved by treating the propellant surface temperature T~urand burning rate rb as the eigenvalues. The iteration starts with guessed T~ur and rb, which are bound by Eq. (30). The condensed- and gas-phase governing equations are solved with these guessed values and other boundary conditions. If the resulting temperature gradients do not satisfy the interracial energy balance equation, Eq. (29) is used to correct the values of Tsur and rb by means of a bisection method. The updated T~.r and r~, are then substituted into the governing equations for another solution of the temperature field. The iterative procedures are performed until Ts,,. and r~ converge, and Eq. (29) is satisfied. Finally, a solution at the physical time level is obtained when all the governing equations and associated boundary conditions are satisfied. In general, the gas-phase solver takes much more computational time than its counterpart for the condensed phase, due to the complexity of the chemical kinetics in the gas phase.
315 Calculations of chemically reacting flows often encounter numerical stiffness problems attributed to the wide variety of time and length scales associated with chemical reactions and transport processes. The problem can be effectively circumvented by using a combined Newton-iteration and (pseudo-) time-integration scheme originally developed by Kee et al. [77]. The Newton method works efficiently for linear systems but may fail to converge for nonlinear systems unless a reasonable initial guess is provided. Conversely, the (pseudo-) time-integration technique is more robust, but less efficient. To optimize the benefits of these two algorithms, computations usually start with the Newton method, and then switch to the time-integration scheme when the iteration fails to converge. After another trial solution is obtained with several time-marching steps, the Newton method is resumed to gain efficiency. The time step in the time-integration technique is sufficiently smaller than the physical time step in order to handle the numerical problems caused by the highly transient phenomena due to rapid chemical reactions. An adaptive-grid system is employed to further improve the convergence rate. A four-step Runge-Kutta method is used for temporal integration of the condensed-phase conservation equations, along with a second-order central differencing scheme for spatial discretization. Calculations start with an estimate of the temperature profile, obtained by solving an inert energy equation. The conservation equations of mass and species concentration are then integrated with the given temperature profile. The energy equation is subsequently solved with the newly obtained void-fraction and species concentration profiles to update the temperature profile. Since these equations are solved sequentially, iteration is required to get a converged solution. Once the temperature reaches the melting temperature, the movement of the solidliquid interface is determined from Eq. (31). The fixed-grid Eulerian method is employed for interface tracking. 4. DISCUSSION O F M O D E L R E S U L T S The theoretical model and numerical method outlined in the above sections were implemented to study steady-state combustion of nitramine monopropellants [33.34], laser-induced ignition of RDX [39,40], and steadystate combustion of nitramine/GAP pseudo-propellants [37-39]. The analyses were carried out over a broad range of operating conditions. Various important burning and ignition characteristics were investigated systematically, with emphasis placed on the detailed flame structure and the effect of the subsurface two-phase layer on propellant deflagration.
316 4.1. S t e a d y - S t a t e C o m b u s t i o n o f N i t r a m i n e P r o p e l l a n t s
Figure 7 shows predicted temperature distributions at several ambient pressures using the gas-phase chemical kinetics mechanism proposed by Yetter et al. [26]. The temperature increases monotonically from its initial value of 293K, and levels off at a value close to the prediction by the chemical equilibrium analysis. The final flame temperature increases with increasing pressure, whereas the flame-standoff distance exhibits an opposite trend owing to enhanced chemical-reaction rates at high pressures. No evidence is obtained of the existence of a temperature plateau in the dark zone regardless of pressure, which is consistent with the experimental observations of self-sustained combustion of RDX monopropellant [41 ]. It is worth noting that a dark-zone temperature plateau (at T 1500 K) was present in the laser-assisted combustion of RDX, while the existence of the dark zone was not evident in the self-assisted combustion. Liau and Yang [41] indicated that the chemical preparation and fluid transport time~, of the intermediate species produced in the primary flame must be comparable in order to form a dark zone.
3500
9
!
.
.
!
3000 v
.
"'"
.
!
'
9
-.
: 913 .
20 5
.
.
.
-
2500
~:1. 2000 1500 ooo
500
,
-o.o
ropellant surface 0.5
1.o
Distance a b o v e propellant surface, mm
Fig. 7 Temperature profiles of self-sustained RDX combustion at various pressures Figure 8 shows the burning rate as a function of pressure. Good agreement between predictions and measurements is obtained. A power law of the burning rate vs pressure is observed, rb = a p
n
(34)
where the pressure exponent n is about 0.83 (with p in atm), and the preexponential factor a equals to 0.3 cm/s for Ti = 293K. The increased burning
317 rate with pressure is attributed mainly to fast gas-phase exothermic reactions at high pressures and their influence on heat transfer to the condensed phase. 101
E O
.~
10~
- ~, 9 O 9
Prediction Zimmer-Gailer (1968) Glaskov (1974) Zenin (1995) _~
rr c cL _
o...
m
1
Tir~,w=293K 100
101 Pressure,
10 2
atm
Fig. 8 Effect of pressure on strand burning rate of RDX monopropellant; self-sustained combustion. The temperature sensitivity of burning rate defined in Eq. (35) is also examined, giving the result shown in Fig. 9.
=I(~r6)lr6~ I()(lnrb)~ P L-~ ~j~= ~ ~ The temperature sensitivity •p
(35) stays around
0.0028 K j for most cases. At
elevated pressures, the heat feedback from the gas phase to the condensed phase is higher, and thus the effect of initial temperature on the interfacial energy balance becomes less important. A numerical analysis on the temperature sensitivity for low-pressure conditions was further performed by Beckstead and co-workers [35]. The predicted temperature sensitivity was determined to be too low compared to the measurements, mostly due to the uncertainties associated with the treatment of the condensed phase in the model. A similar approach was applied to study the combustion characteristics of HMX monopropellant. A detailed description of the theoretical formulation and results is available in Ref. 37. Figure 10 shows the pressure sensitivity of the HMX burning rate. Good agreement was obtained with the experimental measurements by Zenin [11] and Atwood et al. [21]. The pressure exponent n in Eq. (34) was about 0.88, with the pre-exponential factor a equal to 0.35 for Ti = 293 K. The temperature sensitivity of burning rate defined by Eq. (35) at various pressures is shown in Fig. 11. There were noticeable discrepancies
318 between the measured and predicted values at pressures below' 20 atm, a phenomenon that may be attributed to the uncertainties in modeling the condensed-phase heat release process. More detailed understanding of the chemical kinetics in the condensed phase is required to improve model predictability, especially for low-pressure cases in which near-surface exothermic reactions play a more dominant role in determining propellant surface conditions than the heat feedback from the gas phase.
0.005
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . . . . . .
"7,
v, 0.0o4 . ...,,
.'~ dl
0.003
r
0.002 t,'l
E 0.001 100
..................... 101
102
Pressure, atm
Fig. 9. Temperature sensitivity of RDX burning rate; self-sustained combustion.
lOl~ -
'
. . . .
,,,I'
Exp.
(Atwood
'
'
. . . . . .
-~
,
. . . . .
02
E []
~
lOU
C
et al. [21 ])
,
i r e-
it_ / 10"21~u
..........
, 101 p, atm
,
Fig. 10 Pressure dependence of burning rate of HMX monopropellant; self-sustained combustion.
319 7 ~
%
, . . , , , , , ,
6
._r
5 4 t-
~ 0
'
9
9
9U ~
"1'
*
'
~
I
'
'
'
'
I
'
;
'
'
Exp. ( A t w o o d et al. [21]) Current Model
r
i
3
o,-,
.~-
2
.,,.,
~
r~
l 0 i-
1
,,
~
20
....
1
40
60
80
100
p. a t m
Fig.
1 1 Temperature
sensitivity
of buming
rate of HMX
monopropellant;
self-sustained
combustion.
In this chapter, the model results pertaining to the combustion-wave structure of RDX monopropellant are focused. A comprehensive description of theoretical formulation and results for combustion of HMX monopropellant can be found in Ref. 27. The calculated species-concentration profiles were validated against experimental data [22], which was obtained by means of a time-of-flight mass spectrometry technique at 0.5 atrn, as shown in Fig. 12. Good agreement was obtained except for the region next to the surface. The discrepancy may arise from the ambiguity in determining the location of the propellant surface in experiments. Due to the limitation of the spatial resolution (500 Bm), the diagnostic work defined the surface as the location where RDX was completely consumed. This analysis, however, predicted that an appreciable amount of RDX still existed at the surface since only limited RDX decomposition occurred in the subsurface region. If the spatial distribution of the calculated data was artificially shifted upward to the location where NO and HCN attained their peak values, then an improved agreement between the prediction and the measurement could be achieved. The species-concentration profiles revealed that the overall reaction mechanisms globally consist of three steps: (1) decomposition of RDX to CH20, HCN, NO2, etc. near the surface, (2) first-stage oxidization which includes formation of NO and H20 as well as removal of NO2, and (3) second-stage oxidization which includes conversion of HCN and NO to the final products such as CO, N2, and H2. It is worth noting that the highly exothermic reductions of HCN and NO usually occur at elevated temperature (T-- 2000 K) owing to the large activation energies required to initiate these reactions, which provide the major heat source for raising the
320
flame temperature to its final adiabatic value. The calculated molar fractions of the final product species are quite consistent with the chemical-equilibrium predictions, with the deviation being less than 2%.
Theoretical Calculation 0.40
. . . .
I
. . . .
I
. . . .
!
. . . .
I
. . . .
I
. . . .
1
. . . .
0.35 N2 0.30
.s
tT.
/ " ..... ~ . . . . . . . . / -
(i..;
0.25 0.20
."
~'./
/.,~..
~.;,
0.15
CO
/ ; : : " : ' " ".......... -
.4
i
(1)
_.
J
",,i.4....
.."
0.10 o " " "
~
%%"%'"... %
o S
"...
0.05 0.00 -0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Exp. Measurement (Korobeinichev, 1985) 0.40
....
, ....
, ....
, ....
, ....
, ....
, ....
0.35 r O 9. ~
0.30
t'zl "- 0 . 2 0 U.. "~
H20
o
---o
0.25
~'~'~~
0.15
/
:E
~~
0.10 0.05
~
r
Y~~('... 9
.,O ~ O "
"""
x .... x .... 0.00 . . . . -0.5 0.0 0.5
CO
x~.
'~~-,..... ...... NO HC,,~ - - ~ ...........~ ..............o .t . . . . 1.0
"-,,'."7":-9-=--,.._.._J. . . . . 1.5
2.0
2.5
3.0
Distance above propellant surface, mm Fig. 12 Distributions of major species concentrations of self-sustained combustion of RDX at 0.5 atm.
The combustion wave structure at 100 atm is shown in Figs. 13 and 14, exhibiting a close similarity to that at 1 atm except for the shorter flamestandoff distance (6 vs. 600 gin) and molten-layer thickness (2.1 vs. 66 l.tm).
321
The major difference lies in a smaller void fraction. The shorter molten-layer thickness and higher burning rate yield a shorter residence time for condensedphase reaction. Also. high pressure tends to retard the RDX evaporation, which dominates the gasification process in the two-phase layer. As evidenced by the large ratio of HCN to CH20 mole fraction, the endothermic decomposition, (R2), appears more profound at high-pressure conditions. This can be attributed to the higher surface temperature and heat transfer into the condensed phase.
3500
........
, .....
....,
....
, ....
, ....
f
3000 v
2500
d =
2000
l,.
4,,,*
p = 90 aim
4)
el. 1500
E
T i = 293 K rb = 12.0 mm/sec
10oo 500 !
,
,
,
-0.005
0.40
.
.
.
.
.
-0.000
.
.
.
0.35
.
.
I
.
.
.
.
0.005
.
I
.
1
.
.
.
.
0.010
.
.
.
I
9
I
.
.
.
0.015
9
-
9
I
.
.
.
!
.
,
.
0.020
.
.
1
.
.
.
1
t
,
.
0.025
.
.
!
.
.
,
0.030
.
.
RDX N2
g
0.25
"~. ........
/
LL 0 . 2 0 4)
I--HC~]
CO
,,,
o.15
!i//
0.10
0.05
j
0.00 -0.005
o I
"" '~i.
H2
~'..
~
... NO
7 .,2 ~ -0.000
0.005
..- :, . . . . O H , 0.010
0.015
0.020
0.025
0.030
Distance above propellantsurface, mm Fig. 13. Distributions of temperature and major species concentrations of self-sustained RDX combustion at 90 atm.
322
_ . . . .
,
. . . .
,
. . . .
..,
. . . . .
.
1.00
.~,j
700 p = 90 atm T i = 293
6O0
K
~
0.75
= o
L_
0.50
500 E
melting
~" 40o 300
point
F ~
. . . .
-0.004
,.
-0.003
'." 9 9 ,
-0.002
. . . .
",
-0.001
.....
0.25 0.00 -0.000
. . . . . . . . . . . . . . . . . . .
-0.005
1.00
Void
.L.''-
"'
0.20
",~
to o
X a n"
O
HCN :~ 4,,t -= 9 ., NOz,NO,H20 .._._~ / ]o.10 .~_r
u_ o
r
~ \Itit o.15 =u_
RDX
0.75
u. .'g_ o >
0.50
CH20,N20
0.25
0.00 9 -0.005
. . . . . . . . . . . . . . .
-0.004
-0.003
-0.002
.......
/ Y "~
Q.
r.n
\ I~/, 7 0.05 (D,_
~
.
-0.001
,~I 0.00 -0.000
Distance underneath propellant surface, mm Fig. 14. Close-up view of temperature and species-concentration profiles in subsurface region at 90 atm.
4.2. Laser-InducedIgnitionof RDXMonopropellant The entire laser-induced ignition process of RDX in an argon environment has been studied in detail [39,40]. Figure 15 shows the predicted temporal evolution of the temperature field at an incident laser heat flux of 400 W/cm 2 under atmospheric pressure. The initial temperature is 300 K. The interface between the subsurface and gas-phase regions is set to be x = 0, with negative and positive values of the x-coordinate representing the subsurface and gas phase, respectively. The surface temperature is rapidly increased to 475 K within 1 ms, due to the high intensity of laser heat flux. The profiles for t < 1
323
ms represent inert heating of the thin surface layer with conductive heat losses to both the solid- and gas-phase regions. The temperature rises in the gas phase at t = 2 ms are primarily caused by radiant energy absorption rather than exothermic reactions, because the extent of RDX decomposition in the gas phase is very limited at this stage of the event. At t = 2.9 ms, exothermic gasphase reactions start to occur, and a flame appears near the propellant surface at t = 3 ms. During the time period between 3 and 6 ms, the temperature continues to increase to around 1500 K, as a consequence of the heat release by exothermic reactions. As time further elapses, a luminous flame appears, and the temperature rises to its adiabatic temperature. The luminous flame is not stationary but regresses toward the surface. There is a time lag (about 4 ms) between the first appearances of the primary and secondary flames.
3500 3O00 ~-
,
:~ 2500 }-,s E
~
Propellant
'
7.25 ms
~ 7
ms
_
-~
L-- 2OO0I .~ 1500 1000 I 500 1 0.0
0.5
1.0
X, c m
Fig. 15 Evolution of temperature field during laser-induced ignition of RDX in argon at p = I a t m a n d Q~" = 4 0 0 W / c m 2.
Figure 16 shows a close-up view of the temperature evolution in the condensed phase near the propellant surface. The transient development of thermal-wave penetration into the subsurface region is clearly observed. The characteristic thickness of the thermal layer in the subsurface region is much thinner than that in the gas-phase region. Phase transition from solid to liquid can be indicated by the distinct change of temperature gradient at Tm = 478 K. Since most of the CO2 laser heat flux is absorbed by the thin surface layer due to the high absorption coefficient (2800 cm ~) of RDX at the wavelength of 10.6 ~tm, the formation of the mushy zone can be safely ignored. However, some propellants, including RDX, are quite transparent to plasma irradiation in the UV/visible wavelength range; thus, the appearance of the mushy zone may be
324 evident in that situation. Figure 17 shows the distributions of void fraction and species concentrations in the subsurface two-phase region when ignition is achieved at t = 7 ms. The extent of R D X decomposition in the condensed phase is very limited during the laser-induced ignition process up to 7 ms over the range of conditions studied, due to the short residence time and low temperature conditions. The molten layer in the subsurface region is not fully established within this time frame under atmospheric pressure. As indicated in the previous subsection, the steady-state combustion model predicts that the gas bubbles occupy about 45% of the volume at the surface under atmospheric pressure during self-sustained R D X combustion as a result of R D X evaporation and decomposition [34]. However, the surface void fraction during the selfsustained R D X combustion decreases significantly with increasing pressure [34]. 550 __
- "
i
- A m b i e n t Gas: A r ///J
500 d 450 m
6
~-400V
E
k
-~
4 ms
350 r
3~
': /
3 ms
-75
-50
9 ms
0
x. lam
Fig. 16 Close-up view of temperature evolution in subsurface region during laser-induced ignition of RDX at p = 1 atm and Q~,,, = 400 W/cm-'.
325 550
1.2L d
RDX x ! 000
1.01
~. 0.8~
Liquid Solid
j
1 500
~ 450 ._6
c > 0.6 =~ _
Meltin~ Point = 478 K
e--
400 ~ [..., HCN-~///
.~ 0 . 4 _
,~ 0.2~
t
~ Ambient Gas: Ar
0.0
e.,
CH.O.N.Oy
. . . .
i
-20
,
~
~o~
NO 2, N ~
,
i
,
,
,
9
- 15
i
- 10
. . . .
-5
350 0300
x, rtm
Fig. 17 Close-up view of temperature and species-concentration profiles in subsurface region at t = 7 ms (p = 1 atm and Qw~,= 400 W/cm2). The overall gaseous RDX ignition process can be divided into five distinct stages: thermal decomposition, first oxidation, chemical preparation, second oxidation, and completion stages. In stage I, RDX decomposes to lowmolecular weight species, such as CH20, N20, NO2, HCN, and HONO. This decomposition process is slightly endo-/exo-thermic or thermally neutral depending on the initial temperature. In stage II, oxidation reactions occur and release a significant amount of energy with the temperature reaching about 1500 K. The dominant net reactions in stage II can be given as follows. CH20 + NO2 => H20 + NO + CO HNO + HONO => H20 + 2NO 2HCN + NO2 => C2N2 + NO + H20 CO + NO2 => CO2 + NO 2HONO => NO + NO2 + H20 2NO2 => 2NO + 02
(-44 kcal/mol) (-23 kcal/mol) (-33 kcal/mol) (-53 kcal/mol) (8 kcal/mol) (29 kcal/mol)
(R4) (R5) (R6) (R7) (R8) (R9)
The heat release in stage II is mainly caused by the conversion of CH20 and NO2 to H20, NO, and CO, and to a lesser extent by the reactions of HCN and HONO. Stage III represents the chemical preparation time before the second oxidation reactions (stage IV) take place. The species formed in stage II are relatively stable, due to the high activation energies of their associated reactions, and require a finite time to oxidize further. The highly exothermic reactions occurring in stage IV may be attributed to the following net reactions.
326 2HCN + 2NO => 2CO + 2N~ + H, N~O + H~ => N~ + H~O C2N2 + 2NO => 2CO + 2N2 _
(-158 kcal/mol) (-78 kcal/mol) (-169 kcal/mol)
(R10) (R11) (R12)
The reduction of HCN and NO to N2, CO, H20, and H2 is largely responsible for the heat release in stage IV. Finally, all the final products are formed; no further reactions occur in stage V. Figures 18 - 23 show the temperature and species-concentration fields in the gas phase at various times. At t = 2 ms, the gas temperature increases by more than 300 K, although only a small fraction (less than 10 %) of the laser energy is absorbed in the gas phase. This is not surprising, because the heat capacity of the gas mixture is much lower than that of the condensed mixture. At t = 2.9 ms, small amounts of intermediate species, such as HCN, NO, HONO, CH20, N20. and NO2, result from thermal decomposition of RDX. The temperature rises to more than 800 K within 1 mm above the surface. Figure 10 shows the first appearance of the primary flame at t = 4 ms. The aforementioned RDX decomposition products, especially CH20 and NO2, undergo rapid reactions, which leads to the formation of NO, HCN, H20, CO, and N20 in the flame. The dominant net reactions in the primary flame zone can be given by (R4-R9). The temperature increases to about 1400 K. The species formed in the primary flame are relatively stable due to the high activation energies of their associated reactions, and require a finite time to oxidize further. At this stage, the fraction of laser absorption decreases significantly because of the rapid consumption of RDX. which is considered to be the only species absorbing a noticeable amount of laser energy in the gas phase. Figure 21 shows more details of the chemistry involved in the primary flame. The conversion of CH20, NO2, and HONO to NO, CO, HCN, etc. appears to be the major chemical mechanism releasing thermal energy. Figures 22 and 23 show the development of the secondary flame at t = 7 and 7.25 ms, respectively. The temperature increases from 1500 to 3000 K at this stage, and the heat release can be largely attributed to (R10R12). The conversion of HCN and NO to the final products seems to be the dominant net reaction in the secondary flame. Once the secondary flame appears, the intense energy release and heat transfer causes the flame to regress toward the propellant surface.
327
1.0 ~_ 0.9~-
800 t=2ms
o.8F 0.7 L
-'2 ~-u o.6 ~-
700 / ,
600
0.5 0.4
0.3F
500 E [.-,
,
400
0.2 0. I
RDX !
0.00
0.05
O. 10
O. 15
i
i
9
|
0.20
X, c m
Fig. 18 T e m p e r a t u r e a n d s p e c i e s - c o n c e n t r a t i o n p r o f i l e s in g a s p h a s e at t = 2 ms.
l.OF
"'
t i
0.8 ,- O.7 -?- 0.6
1000 900 800 :~
7oo
~
600
E
0.5 "-6 0.4 0.3
500 ~
0.2 400
O.l 0.00
0.05
0.10
0.15
0.20
X, c m
Fig. 19 T e m p e r a t u r e a n d s p e c i e s - c o n c e n t r a t i o n p r o f i l e s in g a s p h a s e at t = 2.9 m s .
328 2000
iOL 0.9~ 0.8 1 RDX 0.7
t=4ms
A
1750
/
1500~d
"~ 0.6 I
1250
0.5
!000 ~-
O.4 0.3 0.2 0.1
750 500
0.0
0.5 X, c m
Fig. 20 Temperature and species-concentration profiles in gas phase at t = 4 ms. 0.08 ~ E 0.07 ~
CH,O
CO
0.06 ~ N~O ~ ~ - ~ N 0.05 L HONO_ "-r u X _ ,~ NO, 0.04
F
. . . . . a 2000 t=4ms 1 1750
20
/// / / ) i \
1500 !250 ,~
co,.
I
0.02
750
0.01 ~
500
0.00
0.01
0.02
0.()3 0 . 0 4 0 . 0 5
0.06
0.07
x, cm
Fig. 21 Close-up view of temperature and species-concentration profiles in primary flame zone at t = 4 ms. A parametric study for investigating the effect of the absorption coefficient of vapor RDX on the overall ignition process has been performed by varying the absorption coefficient by 15 %. As shown in Fig. 18, the gas-phase temperature is rapidly increased by more than 300 K at t = 2 ms, with a small amount of the laser energy absorbed by the gas phase. At t = 2.9 ms, the gasphase temperature rises to more than 800 K, caused by the heat release from the exothermic decomposition reactions in the gas phase. After the inert heating, the heat release from the exothermic reactions becomes much more pronounced than the laser energy absorbed by the gas phase. Since only a small amount of the laser energy was absorbed by the gas phase, a change by 15 % in absorption
329 coefficient did~not influence, the inert heating time significantly. Overall, the effect of the absorption coefficient of vapor RDX on the CO2 laser-induced ignition was not noticeable over the parameter range studied herein.
1.0 !t 0.9
3500
t = 7 ms
0.8
3000
RDX
0.7 [-i
_,.~c'7--"
2500~:
".~ 0.6 0.5
2000 "~
0.4 0.3 0.2
1500 t--, ! 000
0. !
500
0.0
0.5
1.0
X, cm
Fig. 22 Temperature and species-concentration profiles in gas phase at t = 7 ms.
1.0 0.9
t = 7.25 ms
( ~
3500 3000
0.8 0.7
2500:~
"~ 0.6
2ooo .~
:~~~~ ! ~, 0.4
l ,
0.3
o e-
1500 '-
N, / CO
NO
,
0.2
OH
0,
A
-
\., ~------~---~
0.0
l
0.5 x, cm
',
.
.--7--"7_--
1000 500 1.0
Fig. 23 Temperature and species-concentration profiles in gas phase at t = 7.25 ms.
Figure 24 shows the evolution of the CN concentratiorL field. A noticeable amount of CN is observed at t > 7 ms. The concentrations of CN are usually small, except in the secondary flame, thereby serving as a good indication of the flame position. Parr and Hanson-Parr [23] conducted pioneering measurements of the transient flame structure of RDX using both UV-visible absorption and non-intrusive planar laser-induced fluorescence (PLIF). The experiments were
330
performed at three intensity levels of CO2 laser heat flux (i.e., 195,402, and 807 W/cm 2) under atmospheric pressure. Figure 25 shows the measured CN concentration profiles at various times for a laser flux of 402 W/cm 2. Comparison between Figs. 24 and 25 shows good agreement in terms of the CN concentration level. The measured ignition delay time (8.6 ms), however, is slightly longer than the predicted value (-- 7 ms), whereas the predicted flamestandoff distance, defined as the location of the peak value of CN concentration profile, is slightly longer than the measurement. 800 c _
,
700
7.25 ms / ! 7.15 ms
r,
," 600 500
i
C
._
400
I
I
E 300
, ..
,
I i
' :
-1
7 ms
i
-6 200 100 1 ,,.-
,
,A
0.0
1.0
0.5 X,
c m
Fig. 24 Predicted concentration profiles of C N at various times.
800 '
'
'
1
,
,
'
,
600
i !
700 9ms 20 ms 10ms ,/\ f~i
~ 5oo
~
8.6 ms
.2= 400 300 200
/
i i
100 0.00
0.25 X,
0
c m
Fig. 25 M e a s u r e d concentration profiles [23] of C N at various times.
Figure 26 shows the calculated and measured ignition delays of RDX induced by CO2 laser under atmospheric pressure. Excellent agreement is
331 achieved between the predicted and experimental data for laser intensities less than 200 W/cm 2. For 400 W/cm 2, the predicted ignition delay matches the measurements by Parr et al. [23] and Lee et al. [78]. However, the measured data of Vilyunov and Zarko [51] do not agree with the model prediction for laser intensities above 200 W/cm 2. Vilyunov and Zarko showed that the ignition delay increases with increasing laser intensity above 200 W/cm 2, whereas the results of the current model as well as Parr et al. [23] and Lee et al. [78] revealed the opposite trend. Vilyunov and Zarko [51] stated that the RDX ignition was controlled by the solid-phase kinetics at low laser intensities (below 200 W/cm2), whereas the gas-phase kinetics along with the liquid-phase decomposition governed the ignition process at high laser intensities. The current model, however, predicted that the gas-phase chemistry controlled the ignition process over the laser intensity range studied. Thus, the ignition delay became shorter at higher laser intensities, because the gasification rate at the propellant surface increased with increasing laser intensity. Vilyunov and Zarko [51] performed their experiment in both nitrogen and air under atmospheric pressure and /bund that the ignition delays were about the same within the measurement accuracy. Lee and Litzinger [78] utilized argon as an inert gas, whereas Parr and Hanson-Parr perform the experiment in air. The differences in ignition delay among these three sets of measured data, especially above 200 W/cm 2, can also be attributed to the variation in RDX sample preparation in each experiment. The RDX samples used by Parr and HansonParr [23] and Lee and Litzinger [78] were pressed military-grade RDX. Information about the samples used by Vilyunov and Zarko [51] was not available. ! 0 ~
~- I0~I t>
.,-
10.2
10.3
9 9 9 t> ,
Vilyunov and Zarko [51] Parr and Hanson-Parr [23] Lee and Litzinger [78] Current Model i
|
100
i
i
i
t> t~
I
l
i
I
|
, I ....
200 300 Laser Intensity (W/cm 2)
IlllJllllll,i
400 500600
Fig. 26 Effect of CO2 laser intensity on ignition delay of RDX monopropellant.
332 In the experiment by Parr and Hanson-Parr [23], a significant time lag was obtained between the first light and go/no-go times (about 85 -- 100 ms). First light was defined as the time when the luminous flame was first detected, whereas go/no-go was the time when a stable flame was achieved without the laser-assisted heating. The model predictions for the first light and go-no-go times, however, were about the same. In the experiments [23], the luminous flame progressed toward the surface immediately after the first light and moved away from the surface after the maximum temperature gradient was achieved near the surface. The model, however, did not predict this type of flame movement. The luminous flame continuously progressed toward the surface until steady-state deflagration was achieved. The discrepancy between model predictions and experimental observations may be attributed to the heat loss to the ambience. The entire ignition process was treated as adiabatic in the model, whereas heat losses from both the gas-phase flame and the condensed-phase region to the surrounding might be significant in the experiments, in which continuous laser heating was required in order to achieve self-sustained combustion by fully establishing the condensed flame. This suggests that during the ignition stage, heat loss in the condensed phase was too rapid compared tO the heat transfer from the gas-phase flame to the surface. The discrepancies among the existing experimental results may be attributed to the uncertainties associated with measurements under different types of experimental conditions. It is clearly evident that more measured data is needed for model validation. Nonetheless, the present model provides detailed insight into the key physiochemical processes involved in the laserinduced ignition of RDX, and can be effectively used to estimate ignition delay, heat release mechanisms, and flame structure.
4.3. Steady-State Combustion of HMX/GAP and RDX/GAP PseudoPropellants Recently, Yang and co-workers performed numerical analyses to investigate the combustion characteristics of HMX/GAP and RDX/GAP pseudopropellants over a broad range of pressure and laser intensity with various compositions [37-39]. Summaries of the model results for both HMX/GAP and RDX/GAP are given below. 4.3.1 HMX/GAP Pseudo-Propellant Figure 27 shows the temperature and species-concentration profiles in the gas phase during HMX/GAP pseudo-propellant combustion at a CO2 laser intensity of 100 W/cm 2 under atmospheric pressure. The ratio of HMX to GAP mass fraction is 8:2. Reasonable agreement was achieved with the experimental data reported in Ref. 3. The temperature rises rapidly from 677 K at the surface,
333 levels off around 1200-1600 K, and further increases to its final value at 2780 K. The flame can be divided into three regions: 1) the primary flame, 2) the dark zone, and 3) the secondary flame. The dark zone is a nonluminous region between the primary and the secondary flame, and is characterized with a temperature plateau. The concentrations of HCN, NO, and H20 in the dark zone appeared to be similar to those of pure nitramine propellants [3]. The rapid conversion of HCN and NO to N2 and CO in the secondary flame zone were successfully predicted. The dominant net reactions in this stage are as follows. 0.35
3000
0.30
It, CO
g
0.25 - HCN 9~" ~ ~"H O ~0.20 - NO :
~ ~
l
~
~
][]
~
l
- 2500 i2000 v~. 1500
~0.15 ~ ~----" = ~------2~0"0.L___._N.-" _ _ - - ~ J ~
~C
H'O H/CN.N,O
o f~tqfl" .... 0
1 1000 ~
co: ],oo co,
\ ~-I
No
. , , 1~ . . . . " 2, . . . . 3~k~.-g--. . . . . 4. . Distance above Propellant Surface, nun
50
(a)
0.40 I0.30
. .HCN . . . . . . . .
'N2 '
'
'
:
.~_ ~o
0.20
NO
H.O
O
0.10
0"000
-
-
,i Distance above Propellant Surface, turn -
2
6
(b) Fig.27 (a) Calculated and (b) measured [3] species-concentration profiles of gas-phase flame of HMX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity of 100 W/cm2. 2HCN + 2NO => 2CO + 2Nz + Hz NzO + H2 ==>Nz + H20
(R13) (R14)
334 C2N2 + 2NO ~ 2CO + 2N2
(R15)
These reactions are highly exothermic and usually take place at high temperatures due to their large activation energies. The predicted flame standoff distance of 3 mm is slightly shorter than the measured value of 4 mm, partly because of the ambiguity in defining the propellant surface during experiments. Figure 28 shows a close-up view of the primary flame immediately above the propellant surface, which extends over a length of 100 ~tm. The dominant reactions in this oxidation stage are R16. R17, and R3. HMX ~ 4CH20 + 4N20 HMX ~ 4HCN + 2(NO2 + NO + H20)
(R16) (R17)
The prediction of N20 concentration was satisfactory compared with the measurement [3]" however, NO2 and CH20 appear to be consumed too fast. Intermediate reactions forming CH20 and NO2 are still lacking in the nearsurface region in order to yield better agreement with experimental results. Conversion of GAP and GAP ~ to N2, HCN, CO, NH3, CH20, CH3CHO, H20, C2H3CHO, C2H4, CH3CHNH, and CH2CHCHNH occurs in a very short distance (---10 btm). The GAP decomposition is a highly exothermic process releasing a significant amount of energy in the gas phase. However, at the same time, the heat feedback from the gas phase to the surface is reduced due to the dilution of reactive species by the GAP pyrolysis gases. The decomposed fuel fragments, such as CH2CHO, C2H3CHO, CH~CHNH, and CH2CHCHNH. further react to form CH3, HCO, C2H3, and HeCN.
~
1500
H C ~ o =
U
HMX
0.2
1200
/ ;"~,O""~
L
- oo
~0. I
_
~_. . . . . . . . . . I )~
~
,5
-z---z- -
~
7 77;Z~-
10 ~
'
. _~-~-Z,._Z>~. -_ 10 ~
~ .
~ ,
, 7,,
~co: -~-~ 1
0:
-03
Distance abovePropellantSurface,lam Fig. 28 Temperature and species-concentration profiles in near-surface region of HMX/GAP pseudo propellant (mass ratio 8:2) combustion at 1 atm and laser intensity 100 W/cm2.
335
The species-concentration and temperature profiles in the foam layer are shown in Fig. 29. An appreciable amount of HMX evaporates to form gas bubbles in this region, but the extent of decomposition through the pathways (R1) and (R2) appears to be limited. On the other hand, most of the GAP compound is consumed to become GAP* and N2, releasing heat to support pyrolysis in the condensed phase. Further decomposition of GAP* according to (R4), however, is constrained due to the low temperature condition. The predicted surface temperature and foam-layer thickness are 677 K and 30 gm, respectively. 0.5
800 r
HMX, u/2
= 0.4'
750
"z 0.3 ~
:~
"~ .q ~ 0.2
~
0
700
-3
GAP,,, 650
:r.
0.1 ~
600
-30
-20
-10
0
Distance underneath Propellant Surface. gm Fig. 29 Temperature and species-concentration profiles in subsurface of H M X / G A P pseudo propellant (mass ratio 8:2) combustion at 1 atm and laser intensity of 100 W / c m 2.
Figure 30 presents the corresponding temperature sensitivity of burning rate. which appears to be independent of pressure and has a value twice greater than that of pure HMX. In general, the effect of preconditioned temperature on propellant burning rate diminishes with increasing pressure and impressed laser intensity. The enhanced heat transfer to the propellant surface due to large energy release and reduced flame standoff distance in the gas phase at elevated pressure overrides the influence of preconditioned temperature in determining the energy balance at the surface, and consequently decreases the temperature sensitivity of burning rate. Figure 31 shows the effect of propellant composition on burning rate at various pressures. The burning rate in general decreases with the addition of GAP. which releases a substantial amount of N2 through the C-N3 bond breaking in the near-surface region. Although the process is exothermic, the pressure of N2 and large fuel fragments dilute the concentrations of surface
336
reactive species, and consequently reduces the rate of energy release from HMX reactions. The heat feedback to the surface decreases accordingly, rendering a lower burning rate. Another factor contributing to this phenomenon is the blowing effect of the GAP compound, which tends to push the primary flame away from the surface. The situation is. however, different at high pressures. The burning rate of HMX/GAP pseudo-propellant with a mass ratio of 9"1 is greater than that of pure HMX for p > 30 atm. i
T
">
4
~
3;-
No Laser Heatin~
F
',-=
>, - r ._ ._ ....,
.~
1 -1 4
o
,o p,
Fig. 30 Temperature 8:2); self-sustained
sensitivity
of burning
80
00
a r m
rate of HMX/GAP
pseudo
propellant
(mass
ratio
combustion.
9
,
,
,
,
,
,
r , !
.
.
.
.
.
,
10 ~ ~.
,
, ] ,, , ,
~
No Laser Heatin~
~ r ~ ~
i.
_,z-
/
~
"
9:1
~ ~ L
10 t;
-I
10:0
/ --
ic~-2
/
~
8:2 73
- ..... l
i
L
,
,
i
i
i
I
10 ~ p, atm
~
~
,
,
,
I 10
I 2
Fig. 31 Effect of propellant composition on burning rate at various pressures; self-sustained combustion. Figures 32 and 33 show the effect of laser intensity on burning rate for several mixture ratios at 10 and 100 atm, respectively. At 10 atm, the burning
337
rate increases with increasing CO2 laser intensity. Although GAP decomposition is highly exothermic, the burning rate decreases with increasing GAP concentration since the fuel-rich pyrolysis products of GAP reduce the flame temperature and move the flame away from the surface. At a high pressure of 100 atm. the intensive heat transfer from the flame to the surface overrides the effect of surface radiant energy absorption. The burning rate thus appears to be insensitive to the impressed laser intensity. The influence of GAP concentration on burning rate exhibits a different trend from that at 10 atm due to the variation of surface temperature, a phenomenon that has been elaborated in connection with the discussion of Fio 31 0.40
[:
. . . . .
,
. . . .
,
. . . .
,
. . . .
,
,
p = !0 atm
0.35 ~
1o-
)_ t..
0.30 ~
~
- - -'~
E 0.25 L-
......
0.20
.. . . . . . . .
_ .........
-~
"~ 0.15 ?-_-
"~
0.I0
E~_
0.05
~
Mass Ratio (HMX:GAP)
....
0.00
I . 1O0
. . .
I
. . . .
9 ,
lo:o 9:1
v ....
8:2
i
-l
. . . .
! 50 200 250 Radiant Energy Flux, W/cm-"
F i g . 32 E f f e c t o f p r o p e l l a n t c o m p o s i t i o n p = 10 a t m .
3.50~
I
o A
I
,
300
o n b u r n i n g r a t e at v a r i o u s C O 2 l a s e r i n t e n s i t i e s ;
. . . . . . . . . . . . . . . . . . . . .
3.25 E- p = 100 atm
Mass Ratio (HMX:GAP)
r-
3.0OE
o a
10:0 9:!
.... * ....
8:2
-
"~ 2.75 ~
-
-~
~" 2.50 E-
-~
~: 2.25 ~ " ~
~ ............
..........
0-- . . . . . . . . . . . . . .
-,i
1.75 ~-
1.50E!.25 ~r
1.00r
-
~ . . . . 100
, . . . . 150 Radiant
F i g . 33 E f f e c t o f p r o p e l l a n t c o m p o s i t i o n p = 100 a t m .
, 200
Energy
. . . . Flux,
on buming
, 250
. . . .
J 300
,~
Wlcm"
r a t e at v a r i o u s C O 2 l a s e r i n t e n s i t i e s ;
338
The effects of laser heat flux and pressure on the burning rate of H M X / G A P pseudo-propellant (mass ratio 8"2) are shown in Fig. 34. The impressed laser flux causes a substantial increase in burning rate at low pressures (e.g., 1 and 10 atm). The effect, however, diminishes at high pressure, since the heat feedback from the gas phase overshadows the surface laser absorption in determining the energy balance at the surface, as shown in Fig. 35. The heat transfer to the burning surface increases almost linearly with pressure. Figure 36 shows the propellant surface temperature as a function of radiant heat flux at several pressures. The trend resembles that for the burning rate shown in Fig. 34. l
i
-
,
:
,
,
i
,
~
9
:
-
-
----1
p = 1 0 0 atrn o
O
1 .+
.-p
=
10
atrn +
"
p
100
=
I
atm
150 200 250 Radiant Energy Flux, W/cm2
300
Fig. 34 Effect of pressure on burning rate at various CO2 laser intensities (HMX/GAP mass ratio 8:2). 10~F----~
!~
p
=
i00 atm
0
-+. -+
9
,,
"= 103 ~ 39 _p -
.~
=
10 a t m
-~
_
10-~p =
I atm
_~
U_.,
92 .
C
10 j '
10 ~)L
,
~
100
. . . . .
,
,
:
.
~
. . . .
,
. . . .
150 200 250 Radiant Energy Flux, W/cm"
,
300
,
Fig. 35 Heat feedback to propellant surface at various CO2 laser intensities and pressures (HMX/GAP mass ratio 8:2).
339
The melt-layer thickness and surface void fraction are shown in Figs. 37 and 38. respectively. They both decrease with increasing radiant heat flux at low pressure, but remain almost fixed at high pressure. It should be noted that the bubble formation rate can be enhanced with increasing temperature, but may also be reduced by the decreased residence time resulting from the increased burning rate at high temperature. The present case shows a net decrease in the surface void fraction with increasing pressure.
850 F 825 ?,s 800 i :~ ~ 775
p = 100 atm
O
o
.O
750 .'-3
p = 10 atm
"" 725 ~2-- 700 ~_
p = ! atm
675 ~650
-~
~
~ .
. . 1O0
.
. 150
200
250
300
Radiant Energy Flux, W/cm 2
Fig. 36 E f f e c t o f C O 2 laser i n t e n s i t y on s u r f a c e t e m p e r a t u r e at v a r i o u s p r e s s u r e s ( H M X / G A P m a s s ratio 8:2).
It'~lU2 ~
1
'
E•.•.•tm ~-
L !
o_____.____.p= 10atm
~= 101
t-
i
1-
I
p = 100 atm
0
l 0~ [ ' ,
1O0
.
.
.
.
t
150
;
0
~
i
a
I
200
0
i
m
A
i
I
250 Radiant Energy Flux, W/cm-"
~
a
i
,
!
,
300
Fig 37 E f f e c t o f C O 2 laser i n t e n s i t y on m e l t - l a y e r t h i c k n e s s at v a r i o u s p r e s s u r e s ( H M X / G A P m a s s ratio 8:2).
340 10 ~ C
-
_
I
,
'
~
'
"
I
'
-
*
'
I
:
"
,
9
I
'
'
'
'
i
'
p = I atm
-I
.,
p = 10 atm (>
r-
=
L !
p =
o
100 atm o
o
t_
i
| &in--'t 1,j
-
,
100
. . . .
I
150
~
.
J
,
I
200
:
,
,
I
250
,
.
,
,
~
,
300
Radiant Energy Flux, W/cm:
Fig. 38 Effect of CO2 laser intensity on surface void fraction at various pressures (HMX/GAP mass ratio 8:2). 4.3.2 RDX/GAP Pseudo-Propellant In general, the results from the RDX/GAP combustion model described in Ref. 38 show good agreement with the measured burning rates at atmospheric pressure. The measured burning rate of RDX/GAP pseudo propellant with a mass ratio 8:2 was 0.8 mrn/s at 1 atm with a CO2 heat flux of 100 W/cm 2. The calculated value at the same condition was 0.88 mm/s. At 300 W/cm 2, the measured and predicted burning rates were 1.9 and 2.18 mm/s, respectively. The flame structure observed in experiments using TQMS [3] was also reasonably well predicted by the model. Figure 39 shows the predicted and measured [3] species concentration profiles in the gas phase at 1 atm and 100 W/cm 2. Similar to the HMX/GAP combustion, it is found that HCN, NO, and H20 are the major intermediate products in the dark zone. The conversion of HCN and NO to N2 and CO dominates the luminous flame while the consumption of formaldehyde, NO_,, and N20 accounts for the primary flame above the surface. In contrast to RDX combustion, a noticeable amount (1-2%) of CH3CHO was observed near the surface. Here, the agreements between the predicted and measured concentration profiles of CO, CO2, and formaldehyde are not as good as the others. Chemical equilibrium calculation was also performed. This calculation result matches the model output but not the experimental data. Even though the agreement between measured and computed burning rates is reasonably good, further investigations into the combustion wave are suggested to resolve the discrepancy in flame structure.
341 0.4
r--
.o....
C
0.3 ~-
HeN NO
u_
o
H20
0.2
.(1)
c.~ oo
/ ~
N.,O
o.1
00
1
2
3
H O
4
5
x, m m
(a)
0 . 4 r-
=
o_
~
N2
0.a i
;
t.u
0.2 " oo
.o_ L~
Q.. (.f)
0.1
0~
~
.
.
.
.
1
.
.
.
.
.
.
2
.
.
.
.
.
.
.
3
.
4
x, m m
(b) Fig. 39 (a) Calculated and (b) measured [3] species profiles of the gas-phase flame of RDX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W/cm'-. In the foam layer, Fig. 40 shows that the predicted temperature rises from the melt point of RDX at 478 K to around 590 K at the propellant surface. The mass traction of liquid RDX originates at 0.8 and decreases slightly mostly through evaporation and partially through decomposition. The void fraction increases from 0 to almost 9 % due to the formation of bubbles containing vapor RDX and a small amount of decomposed gases. Consistent with the condensed-phase kinetics, the extent of GAP decomposition is negligible at temperatures lower than 600 K. The mass fraction of GAP remains at 0.2 throughout the loam layer, and then evolves into the gas phase. Figure 41 shows the predicted temperature, void fraction, and condensed species
342 concentration profiles in the region immediately above the propellant surface. GAP starts to decompose in the gas phase when the temperature reaches 700 K. At this stage, GAP x is immediately formed due to the elimination of N2 and reaches its maximum concentration within a short distance (less than 0.004 cm). The peak value of GAP" mass traction is less than 10%. The calculated concentration of carbon residue in this case is negligible. If the propellant surface is defined as the location where all condensed species are gasified, the surface temperature would be around 1000 K, consistent with GAP combustion. o.1
6OO
0.09 580
t-
R
E v
0.08 i!
0.07 32
560
0.05
o > "t2 ~-
0.04
co u3
0.06 .,w 540 --
i
O.
E
t.._o
520
o// GAP,/10
~0.03
~ 0 02
/)/
01 -20
-15
9
~
~ CD
~o
X, p m
Fig. 40 Predicted flame structure in the foam layer of RDX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W/cm 2.
1500
1, co .,_, ~_,
Void Fraction
0.8
.
~
~
IJ_ f,~
120O ,,e"
(f) t~
0.6~-
ffl .~ o
0.4
03 0
T
_
~ c~
900 E !_
FGAP ~.
0.2.
0 >
600 _
ol
. . . .
~ -
~
~._.
-.s~, . .
10
x, pm
Fig. 41 Predicted temperature, void fraction, and condensed species concentration profiles in the near surface region of RDX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W/cm2.
343
Figure 42 shows the predicted pressure dependence of burning rate for a RDX/GAP pseudo-propellant with a mass ratio of 8:2. It is found that the burning rate-pressure relation follows a power law which is applicable to many propellants with the exponent n = 1, whereas n = 0.83 for pure R D X . The
exponent value n = 1 indicates that the addition of GAP does alter the combustion characteristics of RDX. Figure 43 shows the temperature sensitivity defined in Eq. (35) of burning rate at various pressures. The temperature sensitivity of burning rate decays at high pressures since the heat feedback is more profound than the effect of initial temperature on the burning rate.
3f~_:: T , = 2 9 3 K '
'
....
~ .... . . ~'"'~{
/
r
[ !
c -~ 133
/ "
0.1
.-
..o.. C r b = a pn a = 0.02 cm/s n=l
. p" /
/
/
/
/
o3
'
lb
'
'2's
....
s'o"~'i'ir 100
p, atm
Fig. 42 Predicted pressure dependence of burning rate of RDX/GAP pseudo propellant (mass ratio 8:2). 0.005
. . . . . . . . . . .
T,, ,
L
,,,,e.
0.00a++ 9, . . 7
t
.~_ ~-
f \'\
\
,.-'~0.003 1 0 >, 0.002
~
s162 o.ool
" \ \ \.
I
o~
'
k ....... " O ~ ' ~ - ~ . ~ . B ......
1'o
'
'2's
. . . . .
....
B.--
5'o'"~'+'ioo
p, atm
Fig. 43 Predicted temperature sensitivity of burning rate of RDX/GAP pseudo propellant (mass ratio 8:2).
344 Similar to results of the HMX/GAP analysis, the combustion characteristics of RDX/GAP pseudo-propellant at various pressures and initial temperatures were investigated [38]. The surface temperature increases linearly with increasing pressure on the logarithmic scale, but it is not very sensitive to the initial temperature. This is understandable because the surface temperature is resolved by an energy balance, and the heat flux is strongly dependant on the pressure but not the initial temperature. The adiabatic flame temperature increases with both increasing pressure and initial temperature. The increase is not linear due to the limitation of grid resolution and the non-linearity of chemical kinetics. The melt-layer thickness decreases with increasing pressure but is not sensitive to the initial temperature. In general, the melt-layer thickness decreases with increasing burning rate, but increases with the higher values of thermal conductivity of the propellant. As shown in Fig. 42, the burning rate is linearly dependant on pressure, and thus the pressure dependence of melt-layer thickness is also linear. The initial temperature of propellant does not exhibit a strong effect on the melt-layer thickness, because both the burning rate and thermal conductivity are not very sensitive to the initial temperature. The surface void fraction decreases with increasing pressure, but increases with increasing initial temperature. It is not surprising because the bubble formation strongly depends on the evaporation process, which is retarded at high pressures but enhanced at high initial temperatures. The effects of laser heat flux on the burning rate. surface heat flux, surface temperature, melt-layer thickness, and surface void fraction at pressure levels of 1, 10, and 100 atm were numerically investigated. The burning rate and surface temperature increase with increasing laser heat flux. The effect decays with increasing pressure because the heat feedback from the gas phase increases with increasing pressure. The melt-layer thickness exhibits an opposite trend; it decreases with increasing burning rate, and its decreasing rate is consistent with the increasing rate of burning rate. In contrast to the heat feedback from the gas phase at high pressures, the laser heat flux increases bubble formation, up to 50% at the surface at 1 atm and 300 W/cm 2. The final set of results show the effects of binder mass fraction on combustion characteristics over a broad range of pressure and initial temperature. Here, it is possible to utilize the model to describe experimental observations. For example, the burning rate of pure GAP is higher than that of HMX, but the addition of GAP into HMX lowers the burning rate [24]. In contrast, recent measurements [3] show the enhancement of burning rate by adding GAP into RDX or HMX. Both observations have been reproduced by the model. Figure 44 shows the effects of initial composition and pressure on the burning rate of RDX/GAP pseudo propellants. The burning rate decreases in the case of higher GAP composition because GAP decomposition produces
345
inert gases that dilute the concentrations of surface reactive species, and thus retard the heat feedback from the gas phase, as shown in Fig. 45.
o~
9
'
~- M a s s
ratio (RDX:GAP)
'
------10:0 - . . . . ........
9 10'; --
,
,
, ,
1 , I
,
'
'
'
'
'
"1
'.~1 . / ~
~.~
9:1 8:2
rr 9-c-
10'
rn no laser !
'
10 5
.
. . . . . . . . 1 0. ' 0
.
.
.
.
i
10 2
p, a t m
Fig. 44 Predicted effect o f propellant f o r m u l a t i o n on burning rate at various pressures.
104
. . . . . . . .
~- M a s s ~
.~
- - - . . . . . .........
103.
,
. . . . . . . .
ratio (RDX:GAP)
.............
' '".~
10:0
9:1 8:2 7:3
- " t-"~..--
"
-
ii
37. 102 / / /
/ /
J
/
/
no laser i .
.
.
.
,
~
02
p, a t m
Fig. 45 Calculated gas-phase heat feedback to propellant surface at various composition and pressure levels. It is evident that the heat feedback is a controlling factor for the burning rate in all the cases without laser, because the pressure dependence of burning rate follows the same trend as that of heat feedback. The addition of GAP modifies the slopes (pressure dependencies) in Figs. 44 and 45, but not in a consistent manner. A small amount of GAP (10% by weight) increases the slope and makes the system unstable, while more GAP (30% by weight) restores the slope to the pure RDX case but reduces the burning rate by more than 50%. Figure
346 46 shows the burning rates at l0 atm with various compositions and laser levels. The profiles of mass ratios 10:0 and 9:1 are very close, indicating the burningrate change due to the addition of a small amount of GAP is negligible for laser heat fluxes ranging from 100 to 300 W/cm=. For higher GAP compositions (20 and 30 % by weight), the burning rates decrease at 100 W/cm 2, but increase at 200 and 300 W/cm z. The effect is more profound at low pressures since the conductive heat feedback from the gas phase is of less importance in the case of laser-assisted combustion. More experimental data, however, is required for model validation as well as an improved chemical kinetics mechanism of GAP decomposition. ~'"'~"' .'_ ~ A t ~
' .... p = 10 atm
~ ....
~ ....
'
....
~
'
0.40 t-
-I
i ""
E 0.35_ . ~ 0.30 ~n"
.
. ~ . ~ . ~ - /
v---
.~
/ /
cL_
0 . 2 0 - --
-~
.~.g2- .........
_
c- 0.25 2-
./
--
M a s s Ratio ( R D X : G A P ) ,,- I o
~r "
10:0 -3 9:1
--a--
0.15 0.10:'
.
.... "
~
~ ' 100
.
I
150 Radiant
.
.
,
,
E
200
Energy
,
,
- ~ - -
8:2
~--
7:3
1
.
.
.
250
.
1
-t
~
51
300
Flux, W/cm 2
Fig. 46 Predicted effect of propellant formulation on burning rate at various laser and composition levels.
CONCLUDING REMARKS Comprehensive analyses have been developed and performed to investigate the steady-state combustion and transient ignition behavior of nitramine monopropellants and nitramine/GAP pseudo-propellants. The combustionwave structures of these propellants were numerically studied over a wide range of operating conditions. These models accommodate detailed chemical kinetics and transport phenomena in the gas phase, and thermal decomposition and phase transition in the condensed phase. Parametric studies were carried out to investigate the propellant burning characteristics and chemical pathways, with special attention given to the effects of the subsurface two-phase region on the flame behavior. In general, good agreement between the measured and predicted burning rates as well as their temperature and pressure sensitivities was achieved. The calculated species profiles matched reasonably well with the measurements. The steady-state combustion model was extended to simulate
347 the entire laser-induced ignition process of RDX monopropellant. Emphasis was placed on the ignition delay and key physiochemical processes responsible for achieving ignition. The predicted ignition delay shows good agreement with experimental data. The propellant gasification rate increases with increasing laser intensity, which in turn gives rise to a shorter ignition delay. In spite of the accomplishments achieved so far, several challenges remains to be circumvented. One major difficulty in both experimental and theoretical investigations lies in the treatment of the two-phase near-surface region, which includes an array of intricacies such as thermal decomposition, subsequent reactions, evaporation, bubble formation and interaction, and interfacial transport of mass and energy between the gas and condensed phases. Nonetheless, the existing models provide a solid basis for investigating various underlying processes involved in the combustion and ignition of energetic materials. ACKNOWLEDGEMENTS This work was supported partly by the Pennsylvania State University, partly by the Army Research Office under Contract DAAL 03-92-G-0118, and partly by the California Institute of Technology Multidisciplinary University Research Initiative under ONR Grant No. N00014-95-1-1338. The authors are indebted to Dr. Yeong Cherng (John) Liau for his contributions in developing the RDX ignition and combustion models.
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348
[7] H.H. Krause, N. Eisenreich, and A. Pfeil, Propellants, Explosives, and Pyrotechnics, Vol. 17 (1992) 179. [8] R. Behrens, Jr. and S.N. Bulusu, J. Phys. Chem., Vol. 96 (1992) 8877. [9] C.A. Wight and T.R. Botcher, J. Amer. Chem. Soc., Vol. 114 (1992) 8303. [10] R.R. Botcher and C.A. Wight, J. Phys. Chem., Vol. 97 (1993) 9149. [ 11 ] A. Zenin. J. Prop. Power, Vol. 11 (1995) 752. [12]T.B. Brill. J. Prop. Power, Vol. 11 (1995) 740. [13]E.S. Kim, H.S. Lee. C.F. Mallery, and S.T. Thynell, Combust. Flame Vol. 110 (1997) 239. [14]T.A. Litzinger, B.L. Fetherolf, Y.-J. Lee, and C.-J. Tang, J. Prop. Power, Vol. 11, (1995) 698. [15] S.T. Thynell, P.E. Gongwer, and T.B. Brill, J. Prop. Power, Vol. 12 (1996) 933. [16] C.Y. Lin. H.I. Wang, M.C. Lin, and C.F. Williams, Intern. J. Chem. Kinetics, Vol. 22 (1990)455. [ 17] D.M. Hanson-Parr and T.P. Parr, J. Energetic Materials, Vol. 17 (1999) 1. [ 18] R.A. Isbell and M.Q. Brewster, Propellants, Explosives, and Pyrotechnics, Vol. 23 (1998) 218. [ 19] T.B. Brill. Prog. Energy Combust. Sci., Vol. 18 (1992) 91. [20] R.A. Isbell and M.Q.J. Brewster, Thermophysics and Heat Transfer, Vol. 11 (1997) 65. [21] A.I. Atwood, T.L. Boggs, P.O. Curran, T.P. Parr, and D.M. Hanson-Parr, J. Prop. Power, Vol. 15 (1999) 740. [22]O.P. Korobeinichev, L.V. Kuibida, V.N. Orlov, A.G. Tereshchenko, K.P. Kutsenogii, R.V. Mavliev, N.E. Ermolin, V.M. Fomin, and I.D. Emel'yanov, Mass-Spektrom. Khim. Kinet., (1985) 73. [23]T.P. Parr and D.M. Hanson-Parr, Twenty-Seventh Symp. (International) on Combust., The Combust. Institute, Pittsburgh (1998) 2301. [24] N. Kubota and T. Sonobe, Twenty-Third Symp. (International) on Combust. (1990) 1331. [25]C.F. Melius, in Chemistry and Physics of Energetic Materials (S. Bulusu, Ed.), Kluwer Academic, Norwell, MA, 1990, pp.21-78. [26] R.A. Yetter, F.L. Dryer, M.T. Allen, and J.L. Gatto, J. Prop. Power, Vol. 11 (1995) 666. [27] S.C. Li, F.A. Williams, and S.B. Margolis, Combust. Flame, Vol. 80 (1990) 329. [28] S.B. Margolis and F.A. Williams, J. Prop. Power, Vol. 11 (1995) 759. [29] S.C. Li and F.A. Williams, J. Prop. Power, Vol. 12 (1996) 302. [30] K. Prasad, R.A. Yetter, and M.D. Smooke, Combust. Sci. Tech., Vol. 124 (1997) 35. [31] K. Prasad. M. Smooke, and R.A. Yetter, Combust. Flame, Vol. 115 (1998) 406. [32]M.S. Miller and W.R. Anderson, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, (V. Yang, T. B. Brill, and W. Z., Ren, Eds.), Vol. 185, Progress in Astronautics and Aeronautics, AIAA, Reston, VA, 2000, pp. 501-531. [33] Y.-C. Liau, The Pennsylvania State University, Department of Mechanical Engineering, Ph.D. Diss., 1996. [34] Y.-C. Liau, and V. Yang, J. Prop. Power, Vol. 11 (1995) 729. [35] J.E. Davidson and M.W. Beckstead, J. Prop. Power, Vol. 13 (1997) 375. [36]J.E. Davidson and M.W. Beckstead. Twenty-Sixth Symp. (International) on Combust., The Combust. Institute (1996) 1989. [37] E.S. Kim. V. Yang, and Y.-C. Liau, Combust. Flames. Voi. 131 (2002) 227. [38] Y.-C Liau, V. Yang, and S.T. Thynell, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, (V. Yang, T. B. Brill, and W. Z., Ren, Eds.), Vol. 185, Progress in Astronautics and Aeronautics, AIAA, Reston, VA, 2000, pp. 477-500.
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350
[71 ] R.K. Kumar and C.E. Hermance, Combust. Sci. Technol., Vol. 14 (1976) 169. [72] M. Kindelan, and F.A. Williams, Combust. Sci. Technol., Vol. 16 (1977) 47. [73] S. Ritchie, S. Thynell, and K.K Kuo, J. Prop. Power, Vol. 13 (1997) 367. [74] K. Puduppakkiam and M.W. Beckstead, 37 th JANNAF Combust. Subcomm. Meeting, CPIA Publ. 2000. [75] M.F. Modest, Radiative Heat Transfer, McGraw-Hill, New York, 1993, pp. 438-449. [76] C.J. Pouchert, The Aldrich Library of FT-IR Spectra, Aldrich Chemical Co., Wisconsin, Vols. 1-3, 1997. [77]R.J. Kee, J.F. Grcar. M.D. Smooke, and J.A. Miller, A Fortran Program for Modeling Steady, Laminar, One-Dimensional, Premixed Flames, Sandia Report SAND85-8240, Sandia National Laboratories, Albuquerque, NM, 1985. [78] Y.J. Lee and T.A. Litzinger, Private Communication, The Pennsylvania State University, University Park, PA, 1995.
Chapter 9
Modeling of Nitramine Propellant Combustion and Ignition Eun. S. Kim, Rongjie Yang, and Vigor Yang* *Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 104 Research Building East, University Park, PA 16802, United States of America NOMENCLATURE A A/ A sp
8j C, d,i
cross-sectional area of propellant sample pre-exponential factor of rate constant ofjth reaction specific surface area temperature exponent in rate constant of jth reaction molar concentration of ith species rate of change in molar concentration of ith species by jth reaction
Cpi
constant-pressure heat capacity of ith species
Di Dr, Ej e
effective mass-diffusion coefficient of ith species thermal diffusion ratio of ith species
A
Hf,,~
/-/sub nv
h
h, h}, k~
activation energy ofjth reaction internal energy fraction of laser energy absorbed by gas phase molar heat of fusion molar heat of sublimation molar heat of evaporation enthalpy enthalpy of ith species heat of formation of ith species at standard condition rate constant ofjth reaction
Corresponding Author. Email: [email protected]
295
296 j~PP
N
NR P P v ,eq
(2L "m
Q~d
R. s
T t u Vcof
v~ fv i fvRj
Xi x
mass flux total number of species total number of reactions pressure equilibrium vapor pressure of RDX external laser heat flux volumetric absorption of laser energy universal gas constant sticking coefficient temperature time bulk velocity correction velocity diffusion velocity of ith species molecular weight of ith species mass production rate of ith species mass production rate ofjth reaction mole fraction of ith species spatial coordinate mass fraction of ith species
Greek Symbols
P
/q p 2 &
absorption coefficient absorption cross section of ith species void fraction density thermal conductivity molar production rate
Subscripts 0+
0bw c
fw g id ini I
gas-phase side of propellant surface subsurface side of propellant surface backward reaction condensed phase forward reaction gas phase ignition delay initial condition liquid phase
297 l ---)g m net S
sur t v
from liquid to gas melting net value of evaporation rate minus condensation rate solid phase surface mass-averaged quantity in two-phase region vapor
1. INTRODUCTION Nitramines, including cyclotrimethylenetrinitramine (RDX) and cyclotetramethylenetetranitramine (HMX), are important oxidizer ingredients for solid propellants. These compounds are highly energetic and produce high impetus and specific impulse for gun and rocket propulsion applications. In comparison with ammonium perchlorate (AP), nitramines produce little smoke, toxicity, and corrosion. In order to meet the rising demand for various stringent performance and environmental requirements, the development of advanced energetic materials continues to be of strong interest to the solid-propellant community. Recently, attention has also been given to nitramine compounds with azide-containing energetic binder ingredients, such as glycidyl azide polymer (GAP), 3,3-bis(azidomethly)oxetane (BAMO), and 3-azidomethyl-3methyloxetane (AMMO), due to the unique characters of azide polymers. These highly energetic polymers have positive heats of formation but produce relatively low-temperature flames. Experimental and theoretical investigations of the complex processes involved in the combustion and ignition of nitramine monopropellants as well as nitramine/azide propellants have been a subject of extensive research. In the past decade, a great deal of experimental diagnostic and analytical modeling efforts have been applied to obtain more accurate and reliable data for the thermal decomposition, thermophysical properties, and flame structures of these propellants [1-24]. Significant advancements have been made in the modeling of combustion and ignition of nitramine and nitramine/GAP propellants [25-41]. The work involved the treatment of self-sustained and laser-assisted combustion [25-39], as well as ignition transients [39,40], with detailed chemical kinetics and variable thermophysical properties. The results have provided direct insight into the underlying mechanisms dictating the entire combustion and ignition processes. The effects of propellant compositions and ambient conditions on burning characteristics and combustion wave structures were examined in detail. This chapter is organized as follows. A short summary of various modeling efforts conducted in the past on nitramine and nitramine-composite propellant
298 combustion and ignition is first given. The state-of-the-art approaches recently developed in this subject area are then described along with a brief discussion of the numerical techniques. Finally, results of these modeling studies are summarized.
1.1.
Modeling
Development
of
Steady-State
Combustion
of
Nitramine
Propellants
The molecular structures of RDX, HMX, and GAP are "shown in Fig. 1. Most of early theoretical analyses of steady-state combustion of nitramine propellants were based on global reaction schemes for gas-phase processes [42]. The first comprehensive model of RDX combustion, accommodating 23 species and 49 reactions in the gas phase, was initiated by Ermolin et al. [43]. The propellant surface conditions, however, were treated as input parameters in order to match experimentally measured species-concentration profiles. A substantial improvement was made by Melius [25] to relax this constraint. His formulation simultaneously took into account the thermal decomposition of RDX and the ensuing chemical reactions to an extent that the key heat-release mechanisms could be identified. Yetter et al. [26] refined Melius' model to include the sub-models of reactions among the major intermediate products such as CH20, NO2, N20, H2, HCN, and NO, but a significant amount of uncertainties still existed about the pathways of the reduction and associated rates of large fragments departing from the burning surface of these cyclic nitramines. By considering global reactions, Margolis, Williams, Li, and coworkers [27-29] developed an analytical approach, which included the presence of gas bubbles and liquid droplets in the two-phase region near the propellant surface by means of methods of matched asymptotic expansion. The model, however, provided limited information concerning the chemical processes. Prasad et al. also studied self-sustained and laser-assisted
O,N /N\
O,N.. H-. ~NO~ C.N" N, c.2
O2N
/N C
CH2
_ /N\No-,
O2N/
N \ c~N\No2
H,
H2
RDX
HMX
1 ' H ~ O--CH--CH2 ;
,
,
OH
{
{ H_,CN--N2 ~ ~ n
GAP
Fig. 1 Molecular structures of RDX, HMX, and GAP.
299 combustion of RDX and HMX [30,31]. Their model differed from the ones described in Refs. 25-29 in that bubble formation within the liquid layer was neglected. In general, these models of RDX and HMX combustion predicted burning rate, surface temperature, and melt-layer thickness reasonably accurately, although some disagreements with experimental data in the nearsurface species profiles and the temperature sensitivity of propellant burning rate were noted. Recognizing the important role of the condensed phase, Liau and Yang developed a detailed model of RDX combustion accounting for the foam layer, which is the region between the gas and solid phases [33,34]. Such a foam layer consisted of two phases: liquefied RDX and bubbles containing gaseous RDX and its decomposition products. Davidson and Beckstead [35] further studied the near-surface temperature distribution and pressure sensitivity of burning rate. The similar approach was later extended to study the combustion behavior of HMX [36]. Studies on the physical properties, sublimation, decomposition, ignition, and self-deflagration of nitramine propellants conducted prior to 1984 are summarized by Boggs [44] and Fifer [45], and the state of understanding of steady-state combustion of nitramine propellants up to 1990 is given by Alexander et al. [46]. A summary of the latest development is covered in a volume edited by Yang et al. [47].
1.2. Modeling Development of Ignition of Nitramine Propellants Ignition of solid propellants and explosives involves an array of intricate physiochemical processes under energetic stimuli, and has been a subject of extensive research since 1950. A comprehensive review of the early work was conducted by Price et al. in 1966 [48]. The experimental and theoretical literature pertaining to the ignition of solid propellants over the period of 1966 through 1980 was reviewed by Kulkarni et al. [49] and Hermance [50]. The state of understanding in Russia up to 1989 was presented by Vilyunov and Zarko [51], giving a detailed examination of the various ignition models and related experimental approaches. In 1998, a review of laser and radiative ignition of 24 solid energetic materials, with emphasis on work performed in the Former Soviet Union. was provided by Strakouskiy et al. [52]. Many theoretical ignition models have been developed to study the ignition of solid propellants and explosives, which can be broadly divided into four categories: solid-phase (or reactive solid), heterogeneous, gas-phase, and multiphase reaction models. The solid-phase reaction models [53-56] assume that exothermic reactions in the condensed phase are the dominant mechanism of ignition, while the effects of surface and gas-phase processes are secondary and can be neglected. Heterogeneous reaction models [57-65] assume that heterogeneous reactions at the propellant surface are responsible for ignition
300 due to the molecular diffusion of ambient oxidizer species to the propellant surface. The formulation takes into account the condensed-phase conservation equations of energy and species concentration along with interfacial boundary conditions. Unlike the previous two categories, the gas-phase reaction models [66-73] presume that exothermic gas-phase reactions and their heat feedback to the propellant surface are the primary mechanism of ignition. Conservation of energy and species concentration in the gas phase is of major concern, but the condensed-phase equations are also included for completeness. In spite of their contributions in correlating experimental data and providing qualitative understanding of ignition behavior, the solid-phase (or reactive solid), heterogeneous, and gas-phase reaction models [53-73] are semi-empirical in nature and do not provide predictive capability at scales sufficient to resolve the detailed ignition mechanisms and flame evolution. A prior understanding of the ignition process is usually required before modeling. This obstacle mainly results from the use of global kinetics schemes derived for steady-state combustion. Moreover, a simple pyrolysis law is often employed to describe the propellant gasification process in terms of propellant surface temperature along with prescribed condensed-phase heat release. Recently, Liau, Kim, and Yang developed a multi-phase reaction model by extending the steady-state model described in [33,34] to include the transient development in the entire combustion zone, including the solid-phase, nearsurface two-phase, and gas-phase regions [39,40]. The formulation accommodates detailed chemical kinetics and transport phenomena in the gasphase region, as well as thermal decomposition and subsequent reactions in the two-phase region. Thermodynamic phase transition and volumetric radiant energy absorption are also considered for a complete description. The model is capable of treating the entire ignition process from surface pyrolysis to steadystate combustion, with the instantaneous burning rate and surface conditions treated as part of the solution [39,40]. A summary of the theoretical formulation and results of this multi-phase model is given in the following sections of the current chapter.
1.3. Modeling Development of Combustion of Nitramine/GAP PseudoPropellants Most of the early work on GAP decomposition and combustion was based on global decomposition pathways [74]. The physiochemical processes involved in the combustion of a cured GAP strand is schematically illustrated in Fig. 2. The entire combustion-wave structure can be segmented into three regions: solid-phase, near-surface two phase, and gas-phase regimes. In the solid phase, the extent of chemical reactions is usually negligible due to the low temperature and short residence time. Thermal decomposition and ensued
301
reactions, as well as phase transition, take place in the foam layer, generating gas bubbles and forming a two-phase region. Rapid gasification occurs at the burning surface, and further decomposition and oxidation continue to take place and release a significant amount of energy in the near-surface region. The burning surface temperature is greater than 700 K. No visible flame is observed in the gas phase" instead, a large amount of fine powder is formed away from the burning surface and generates a cloud of intense smoke. The final flame temperature of GAP is around 1300-1500 K, which is significantly lower than those of nitramines (-- 3000 K).
:t Major Species: ~(~Invisible 1 1i N_,, HCN. CO. CH_,O, NH3. i/Flame l CH~CHO. CH_-CHCHNH. ~.. CH~CHNH. H-O, CHa. C-H~ j) 9 - -~ (Yellow Fine "~ L ~ 9 [Powder (Formed[ 9 . -~"-~.~in Gas P h a s e ) J : Decomposition. Evaporation, " [ and Gas_Phase Reactions (Bubble) 1" " ". " " . " 7",." - 1500 K
:d Phase T,- - 700-800 1050 K [2
Solid Phase ]
Fig. 2 C o m b u s t i o n - w a v e structure of GAP.
In recent years, Yang and coworkers [37-39] have established comprehensive numerical analyses of nitramine/GAP pseudo-propellant combustion to predict the propellant burning rate and detailed combustion wave structure over a broad range of pressure, laser intensity, and propellant composition. The steady-state model described in [33,34] was extended to include GAP binder in the nitramine combustion. The model takes into account various fundamental processes at scales sufficient to resolve the microscopic flame-zone physiochemistry. The thermochemical parameters of nitramine and GAP are deduced from existing experimental data. Four global decomposition reactions in the condensed phase as well as subsequent reactions are included. In the gas phase, a detailed chemical kinetics scheme involving 74 species and 532 reactions is employed to describe the heat-release mechanism. The key physiochemical processes dictating the propellant burning behavior and flame
302 structure were studied over a broad range of ambient pressure, preconditioned temperature, propellant composition, and impressed laser intensity. The model approaches and results for HMX/GAP [37,39] and RDX/GAP [38] combustion will be briefly discussed in the current chapter. 2. T H E O R E T I C A L F O R M U L A T I O N Three physical problems are considered in this chapter: 1) steady-state combustion of nitramine propellants; 2) laser-induced ignition of RDX monopropellant; and 3) steady-state combustion of nitramine/GAP pseudopropellants. During the past decade, Yang and co-workers [33,34,37-41] have developed a series of comprehensive numerical models for studying the key physiochemical processes involved in combustion and ignition of nitramine monopropellant and nitramine/GAP pseudo-propellants. These models accommodated detailed chemical kinetics and transport phenomena in the gas phase, as well as thermal decomposition and subsequent reactions in the condensed phase. The formation of gas bubbles in the molten surface layer due to molecular degradation and thermodynamic phase transition is also included to provide a complete description. The steady-state combustion models [33,34,37-39] are capable of resolving the combustion-wave structures in both the gas and condensed phases, with the instantaneous burning rate and surface temperature calculated as part of the solution. The analyses [33,34] were later extended to treat the entire ignition process from surface pyrolysis to steadystate combustion [39,40].
2.1. Steady-State Combustion of RDX Monopropellant Figure 3 shows the physical model of concern, a strand of RDX monopropellant burning in a stagnant environment with or without the assistance of external laser heat flux. To facilitate formulation, the entire combustion-wave structure is conveniently segmented into three regions: 1) solid phase; 2) near-surface two phase, and 3) gas phase. During burning, the propellant remains thermally stable in the solid phase until the temperature approaches the melting point at which thermodynamic phase transition occurs as shown in Fig. 4. Molecular degradation and evaporation of RDX then take place in the liquid layer, generating bubbles and forming a two-phase region. The propellant subsequently undergoes a sequence of rapid evaporation and decomposition in the near field immediately above the foam layer. Oxidation reactions continue to occur and to release an enormous amount of energy in the gas phase, with the final temperature reaching the adiabatic flame temperature. A detailed description of the theoretical model can be found in Refs. 33 and 34.
303 x gaseous f 38 spec=es flame / 158 or 178 reactions region (Metus, Yeller)
[ ,2 decoml:oSition pathways - I 1 gas-phase reaction ", o. ,%. o~_foam layer~ eva,oorationVcondensation t - L (mi,) pretmated region phase transition T
RDX deco.,m~sition HCN+HONO
3000K
pdmarlfflame~_ NO+CO+N2 seconda~fla_me~ N2+CO+H20
+CH20+N20
+H20+HCN
+CO2+H2
,etc.
,etc.
,etc.
Fig. 3 Strand of RDX burning in a stagnant environment.
gas phase
RDXvapor
Q
c:> o
o
foam layer
o o
o
o
solid phase
Fig. 4 Schematic diagram showing various regions in RDX combustion-wave structure.
2.2. Laser-Induced Ignition of RDX Monopropellant The physical problem of concern is the ignition of a strand of RDX monopropellant induced by a continuous and radially uniform CO2 laser. The physiochemical processes involved are schematically illustrated in Fig. 5. The propellant and the ambient gas are initially at room temperature. Once the laser is activated, volumetric absorption of laser energy in the solid phase takes place, as shown in Fig. 5a. In the gas phase, only certain gaseous species, such as vapor RDX, absorbs a noticeable amount of laser energy at the wavelength of 10.6 ~tm; thus, the gas-phase absorption is negligible during the inert heating period. When the solid reaches its melting temperature, the absorbed radiant energy can not further raise the temperature without first melting the solid. Since the radiant energy absorbed is insufficient for instantaneous melting of all of the solid in a short period, partial melting of the solid occurs, which leads to the formation of a mushy zone consisting of both solid and liquid (Fig 5b).
304 When a pure liquid layer is formed, the solid-liquid interface starts to move due to conductive and radiative heat transfer (Fig. 5c).
I Gas Ph~el
__T2 Ambient ~ Temperature Gas qt,l,.;___w.~t Profile -
-
- ----~-~----
-,"---"--
(a)
Solid
............
Tin,
x'--
l
Mushv
. - - - ~ --~, i ' ~ ' ~ -~ Liquid Ambient ~1~:~ ... Gas ,, - - - - ~ . . I re,it
~
Solid
(b)
t
T*..- Foam Zone - Ambient
Mushy - - zone
~
!! / < t,d
77., X-'---"l
'-Tmelt
TI t
'\ ~
Foam
Zone --~
- oo Mushy
i'-- Zohe
Pyrolyzed ~ ~qh Gas
(d)
~ ~ - - - ' - ~ - '
X "'--
~ T,.,
~_ Tnx:lt
,
-
t
~o
l
T':
\
'l
X'"J
._-2
T
~
~
Foam
Zone ---
t"-- Zone
k-Tmelt \, Foam . ~ Zone --~
u
Mushy
- ~
Mushy
~--Zone ~:l
Solid i t>tid
Fig. 5 Physiochemical processes involved in laser-induced ignition of RDX. In the liquid, thermal decomposition and subsequent reactions, as well as phase transition, take place, generating gas bubbles and forming a two-phase region. The propellant then undergoes a sequence of rapid evaporation at the surface (Fig. 5d). Ignition occurs if the heat flux is sufficiently large to initiate the subsequent self-accelerated exothermic reactions which result in substantial heat release (in the gas phase) and emission of light. A luminous flame is
305
produced, regresses toward the surface, and finally reaches a stationary position corresponding to its steady-state condition. A brief description of the theoretical model is given in the Section 2.4. with detailed information available in Refs. 39 and 40.
2.3. Steady-State Combustion of Nitramine/GAP Pseudo-Propellants Figure 6 shows schematically the physiochemical processes involved in the HMX/GAP pseudo-propellant combustion. A physical model for RDX/GAP pseudo-propellant combustion is available in Ref. 38. The entire combustionwave structure is segmented into three regions: solid phase, near-surface Tt - 2800 K
~Rapid Consumption of ~ L.. HCN and NO J
(MajorSpeciesinDarkZone: N.. H.O. NO. CO. HCN. H.CO. N,O. H.. CO. Td,,,.k ......
--
_~ ~econdary ] " ~ l a m e ZoneA
" ~ ,
Dark Zone
1250 K
., " o ~ (~AP Polymer'i (',... ") ('Decomposition, Evaporation, i~ - ~ " "[Residue ~] - x_A vnmary | [ and Gas-Phase Reactions (Bubble)[ ~ A o ~ 9 "x...Flame Zone fl " -~ ~ - ~ O ~ ' V " ,.~_.~ O__~, (HMXVapor ~,~n v ~ ~ ~L.V ' ~ , ~ b ~ d J l l V ~ q ~ . ' ~ l ~ /Liquid Interface)
(HMX Melt Front) ~
I. SolldPhase ~ HMX
GAP
Fig. 6 Combustion-wave structure of H M X / G A P pseudo-propellant at 1 atm.
two phase, and gas phase. In the solid-phase region. HMX powder and GAP are physically mixed. The former melts at 558 K with negligible chemical reactions taking place, due to the low temperature and short residence time. Thermal decomposition and phase change of HMX occurs in the liquid phase to form a foam layer. The propellant surface (x = 0) is defined herein as the interface between the foam layer and gas-phase region, at which rapid gasification of HMX prevails. Since the surface temperature of HMX/GAP pseudo-propellant (-700 K) is lower than that of pure GAP, GAP leaves the surface as aerosol surrounded with vapor HMX and its decomposed gaseous
306 products. In this region, GAP remains as a condensed species and continues to decompose. A significant amount of carbonaceous residue may be present on the surface during combustion. To facilitate analysis, the coordinate system is fixed at the propellant surface. A quasi one-dimensional model is formulated as a first approximation of the problem. Both the sub-surface and near-surface regions require a multi-phase treatment because of the presence of GAP and other condensed species in these zones. A detailed derivation of the theoretical model is available in Refs. 37 and 39. A similar model approach has been applied for studying RDX/GAP pseudo-propellant combustion [38].
2.4. Conservation Equations A brief summary of the theoretical formulation of physicochemical processes in various regions during the laser-induced RDX ignition process [40] is given below. The model for steady-state combustion can be treated as a limiting case by neglecting all the time-varying terms.
2.4.1 Gas-Phase Processes The formulation for the gas-phase region is based on the mass, energy, and species transport for a multi-component chemically reacting system of N species, and accommodates finite-rate chemical kinetics and variable thermophysical properties. If body force, viscous dissipation, and kinetic energy are ignored, the conservation equations for an isobaric flow can be written as follows. Mass a(pA) + - - (p,,A) = 0, ~t Ox
Species concentration 9A ~~J+Y,p u A OYi +~(9AViYi 0 )= A~'vi ot 0x 0x
(1)
(i = 1,2..... N),
(2)
Energy pcpA~)T~)(pA)+pucAi)T~__~._.(LAi)T~_i~I( ~t ~t P ~x = Oxk, Ox ) a
i)T + r PYiVict, i -~x
, i ] .+, ,AQrad.g (3)
where subscript i denotes the ith species. The specific enthalpy hi is defined by
hi = fir,t c1,,dT + hs,
(4)
Standard notations in thermodynamics and fluid mechanics are used in Eqs. (14). The mass diffusion velocity 5',- consists of contributions from both concentration (i.e., Fick's law) and temperature (i.e., Soret effect) gradients,
307 V,=-D, - -1 ~ X,
+ D
o,~
Dr - 1- ~~
--~'
(5)
+ V
X i T o~x
co,
where the correction velocity Vco, is employed to ensure that N
~ Y E =0
(6)
1=1
The ideal-gas law for a multicomponent system is derived to close the formulation. p = pR, T
•,__,wY
(7)
2.4.2 G a s - P h a s e C h e m i c a l K i n e t i c s
For a set of NR elementary reactions involving N species, the reaction equations can be written in the following general form: kfw I ,V
N
Zv;iM -~i
i = Zv~M,, k bw ! 7-i "= ,
j:
1,2 .....
g R
(8)
where v~ and v~ are the stoichiometric coefficients for the ith species appearing as a reactant in the jth forward and backward reactions, respectively, and M; is the chemical symbol for the ith species. The reaction-rate constant k, (either ke~, or kb,,.' ) is given empirically by the Arrhenius expression
k, = AjT 8 exp(-Ej / R.T)
(9)
The rate of change in molar concentration of the ith species by the jth reaction is N
= ( Tj
9
N
9
1-I c ?
FI c 2 )
i=i
i=i
(lO)
The net rate of mass production of the ith species ~i,i in Eq. (2) is then obtained by summing up the changes due to all reactions: NR
~, = w, ~ dT,j
(11)
j=!
It must be noted that the expression for chemical reaction rates, Eq. (10), is valid strictly for elementary reactions. If a global kinetics scheme is used, the exponents for molar concentrations may differ from their stoichiometric coefficients in order to match experimental data. The detailed reaction mechanism proposed by Yetter [26] and augmented by Lin and co-workers [4] is employed to treat the gas-phase chemical kinetics. The model is developed based on a hierarchical approach for collecting kinetic
308 data and the specific chemical sub-models that are required to form the gasphase combustion mechanism [26]. In particular, three kinetic sub-models of increasing complexity (N20 decomposition, H2/NO2 reaction, and CHa/N20 reaction) are established using the results from kinetics experiments over a broad range of temperature and pressure. When the initial decomposition steps of RDX proposed by Melius [25] are adopted, the overall scheme contains 38 species and 178 reactions. Here, the N-N bond cleavage is assumed to be the first step of the gas-phase decomposition process of RDX due to its weak bond energy of about 50 kcal/mol compared to - 60 kcal/mol for the C-N bond and -90 kcal/mol for the C-H bond. Li and Williams [29], however, indicated that the initial dominant decomposition pathway might be concerted symmetric triple fission to produce three H2CNNO2 fragments at high temperatures. At present, uncertainties still exist about the types of species formed and their associated rates, especially for regions in close proximity to the burning surface. More experimental investigation isneeded to clarify the initial decomposition steps of RDX. In the past. detailed kinetics models have been implemented to simulate self-sustained and laser-induced combustion of RDX under steadystate conditions [33,34]. Reasonably good agreement was obtained with experimental data in terms of propellant burning rate and flame structure. Three deficiencies, however, were observed: 1) insufficient quantities of N2 and NO2 in the first stage of flame, 2) abundance of CH20 at the end of the first stage, and 3) over-prediction of the ignition delay. Modifications were thus undertaken to circumvent these problems in three steps. First, a reaction allowing for the formation of N2 during the initial stage of reaction was added to the model. Second, the rate of thermal decomposition of H2CN was increased to allow for greater H-radical generation and subsequently for faster consumption of CHzO. Third, a reaction between HzCNNO2 and NO2 was added to enhance the ignition process. Recently, Lin and coworkers [4] revised the near-surface combustion mechanism by adding more reactions involved in the consumption of H2CNNO2, H2CNNO, HzCNO, H2CNOH, and H2CN. The kinetic rates of these added reactions were determined using high-level ab initio molecular orbital (MO) and statistical theory calculations [4]. The resulting kinetics scheme, containing 49 species and 250 reactions, can be found in Ref. 39.
2.4.3 Subsurface Two-Phase Processes The liquid and gas bubbles underneath the propellant surface are treated together and referred to as the subsurface two-phase region. The physiochemical processes in this region are extremely complicated, involving an array of intricacies such as thermal decomposition, evaporation, bubble formation, gas-phase reactions in bubbles, interfacial transport of mass and
309 energy between gas and condensed phases, etc. Taking full account of these processes is hardly practical, and many simplifications have been made to render the analysis manageable. A two-phase fluid dynamic model using a spatial averaging technique is employed to formulate the complicated phenomena in the two-phase region [33,34]. The mass diffusion velocities in the two-phase region V,:iand V,; are assumed to be relatively small compared to their convective counterparts in the gas phase, and are ignored to simplify numerical calculations. The conservation equations for both the liquid phase and gas bubbles can be combined into the following form: Mass .
O[(1-O)p,,,,
at
]
+op~
Ox
(12)
-0
Species concentration f o r liquid p h a s e
~)[(1- 0)Pt It, ] *. ~ [(! 0t
0x
(:)p, u t Yti l = ,vii
(i= 1.2..... N t )
(13)
Species concentration f o r gas p h a s e
at
= ,i:g i
F
(i=1,2
.....
Ng )
(14)
a x
Energy ,
a p, c l,., -~t + p'"'c p'' ~Ox -ax _
2, oT'
-~x;
V.
N ~.
Z hlj,i..O Z h, ,i,.
_
:=l
-
j=l
+ Z hgjI:~'i:t~g
(15)
j=l Nc
- ZhljYliWl~g
+Q~ad.l
j=l
where subscript t denotes the mass-averaged quantity in the two-phase region. The source terms, %. and ,~,,, represent the mass production rates of the ith species in the liquid phase and gas bubbles, respectively, and ~i:t_~g represents the mass conversion rate from liquid to gas.
2.4.4 Subsurface Chemical Kinetics a n d Phase Transition
The global decomposition model of RDX proposed by Brill et al. [12], derived from a well-calibrated temperature-jump/Fourier transform infrared (T-
310
jump/FTIR) spectroscopy experiment, is adopted here. includes two pathways as follows" RDX,:.
kl ) 3CH:O + 3N_,O
RDX ,
k: >3HCN + 3HONO
.
This mechanism (R1)
fast -> 3HCN + -3 NO + -3 NO, + -3 H ,O 2 2 2 -
(R2)
Reaction (R1) is an exothermic, low-temperature pathway, whereas reaction (R2) is an endothermic, high-temperature pathway. The reaction rates are obtained tu a model of the T-jump/FTIR experiment [15], which takes into account the heat transfer of the filament and sample. kl = 6"00•
-
36.0 kcal/mol) s_ I
(16)
RuT
~'VRi = ( I -- ~) )ptkl
(
k 2 = 1.60• 1.'t,'R2 --
-
( 1-
45.0 kcal/moi) R,,T
s
_i
(17)
)Ptk2
r
The two global decomposition reactions are nearly thermally neutral at temperatures around 600 K. Subsequent reactions among the products of (R1) and (R2) may occur and provide the energy to sustain pyrolysis. Brill [12] examined several plausible secondary reactions, such as CH20 + NO2, CH20 + N20, and HCN + NO2, and their corresponding reaction rates. Results indicated that the following reaction NO 2 + C H 2 0
(R3)
t~ ~ N O + C O + H _ , O
is probably the most important secondary reaction in the subsurface region. The reaction rate of (R3) has been determined from shock-tube experiments [16] and is given by (
k3 =8"02•
~R.~ =,~.~
-
13-7 kcal/mol) R,,T
P.~ YCH,o P vYNO~ WCH
_, O
cm3 mol-sec (18)
WNO-~ _
In addition to the thermal decomposition and its subsequent reactions (R1R3), thermodynamic phase transition from liquid to vapor RDX is considered to provide a complete description of the mass conversion process. RDX(,, r
RDX,,~,
(R4)
311 Based on gas-kinetic theory, the net evaporation rate is taken to be the difference between the evaporation and condensation rates [33] and is expressed as
rune t = S "~- //'IVRDX
R,,T
/p q_x ox/ p
Thus, the specific mass conversion rate due to evaporation becomes ~'R4 = Aspth2e,
(20)
The specific surface area A,p is a function of void fraction and number density of bubbles, and is derived as follows. Asp =(36mz)ll~O "-13, 0 < 1/2 or (36mz)J13(l-O) 21~, 0 > 1 / 2
(21)
where n is the number density of gas bubbles to be determined empirically [33]. 2.4.5 Solid-Phase Processes Since very little RDX decomposes in the solid phase, due to its low temperature conditions, only the energy conservation equation that includes both conductive and radiative heat transfer is required to model the solid-phase processes. The equation takes the form p, cp..~ --~t + p,u.~c,,.s --~-x= -~-x~ ' -~x + Qrad.,
(22)
where subscript s represents solid. The thermal properties of RDX were recently measured by Hanson-Parr and Parr [ 17]. Since the properties of liquid RDX, such as 21 and c r ~, are not available in the literature, the same values are used for both the liquid and solid RDX. The thermodynamic and transport properties of RDX used in this analysis are available in Ref. 39. 2.4.6 Radiative Heat Transfer The radiative heat transfer processes are complicated and difficult to model, usually including absorption, emission, and scattering of radiant energy in both the gas and condensed phases, as well as surface absorption, transmission, and reflection. In this work, the focus is on a CO2 laser with a wavelength of 10.6 l,tm. The following assumptions are made to render the analysis feasible. First, the CO2 laser is treated as collimated irradiation and locally one-dimensional. Second, reflection at the propellant surface is not considered, since the normal reflectivity of RDX with a refractive index of 1.49 at 10.6 g m was estimated to be only 0.047, using Fresnel's equation [ 18] Third, the levels of scattering by and emission from the gas-phase, two-phase, and solid-phase regions are
312 assumed to be relatively small compared to that of absorption. Finally, Beer's law is employed to determine the volumetric absorption in the solid- and twophase regions as follows. The absorption in the solid and subsurface two-phase regions (x < 0) is Qrad.,. =(1- f~, -Cts,~ )(l-O)fl,.e"-~'P,-~'Q(~e~
(c= liquid, solid)
(23)
where f, is the fraction of laser energy absorbed in the gas-phase region, ~ur the fraction of laser heat flux absorbed by the propellant surface, ,6'~ the absorption coefficient, and Qi~s~r the laser heat flux. The absorption coefficient of solid RDX for a CO2 laser at a wavelength of 10.6 ktm has been measured by Isbell and Brewster [18] to be 2800 cm -~. Since the absorption properties of many types of semi-transparent liquids are quite similar to those of solids [75], the absorption coefficients of solid and liquid RDX are assumed to be the same in this work. The fraction of laser energy absorbed in the gas-phase region fg is defined by the following equation:
fO_;a fg = 0..q___~ Q~'a~er
(24)
where 0,~.~ is the gas-phase absorption of laser energy, and can be estimated by examining the infrared (IR) transmittance data. The vapor RDX IR spectrums obtained using both confined rapid thermolysis (CRT)/FITR spectroscopy [13] and rapid-scanning FTIR spectroscopy [19] show strong, broad absorption bands of vapor RDX in a wavelength range of 4.7 to 13.3 ktm. The absorption characteristics of the gaseous decomposition products of RDX at 10.6 ~m can be readily studied from their corresponding individual IR spectra [76]. None of the major decomposition products exhibits a noticeable absorption at 10.6 ~m. It is clearly evident that of the species present, only vapor RDX absorbs a considerable amount of CO2 laser energy in the gas phase. Thus, volumetric absorption in the gas phase is given by "w
"a
Q~ad.,r = CRDXA,."CRDX.gQl~er
(25)
where CRDX is the molar concentration of vapor RDX, and Av Avogadro' constant. The absorption cross-section of vapor RDX, ~r is defined as rRox~ = ~~. WRDX
(26)
PRDX.,-A,.
Since the absorption properties of vapor RDX are not available in the literature, the absorption coefficient fl~ is used to estimate ~'RDx.s with the assumption that
313 the characteristics of vibration-rotational bands of vapor RDX at the wavelength of interest are similar to those of intermolecular vibration bands of condensed RDX [75]. An IR transmittance spectrum for solid RDX, obtained from the measurement of RDX powder pressed in a KBr matrix [20] shows a strong absorption band of solid RDX at 10.6 ~m, similar to the absorption characteristics of vapor RDX. At present, the use of the same absorption properties for both condensed and vapor RDX seems to be reasonable, due to the lack of measured data. Note that a parametric study has also been performed by varying the absorption coefficient of vapor RDX by 20 % in order investigate the effect-of absorption properties on the overall ignition process.
2.4.7 Boundary Conditions The physical processes in the gas-phase and subsurface regions must be matched at the interface by requiring continuities of mass and energy fluxes. This procedure eventually determines propellant surface conditions and burning rate as the eigenvalues of the problem. The interfacial boundary conditions are expressed as follows:
Mass (27)
(pu) o_ =[(I-~)p/u t +Op~ttg ]o-
Species concentration LO(tt + Vi )Yi ]o + =[(l-q~)PlUIYli + r
(28)
o-
Energy f2dT]
I2 dT]
H,,
(29)
where subscripts 0 § and 0 represent conditions at the interface on the gas-phase and subsurface sides, respectively. Note that Eq. (27) is essentially the summation of mass fluxes of all species governed by Eq. (28), and thus can not be independently used for determining the eigenvalues. An additional condition is required. Here, the thermodynamic phase transition from liquid to vapor RDX is assumed to prevail at the interface, o_,ivin,,
(P,",)o- = 'n,,~,
(30)
Equations (28-30), coupled with the assumptions that Tg = Tl and pg,g = p~ut in the condensed phase, are sufficient to solve the set of unknowns (ut, 7", O, Yi) at the propellant surface. The far-field conditions for the gas phase require the gradients of flow properties to be zero at x ~ oo.
314
O___pp= O t__jt= ~ Y. _- O T -- 0 a t x ~
~x
Ox
~x
oo
(31
)
bx
The condition at the cold boundary for the solid phase (x ~ _oo ) is T = Ti. i
(32)
at x - - ~ - o o
Finally, the conditions for the phase transition from solid to liquid at the melting point (T,,, = 478 K) are required. T , = T, = T,,,
and
(33)
k ~T.
=k ~,
p,n,.,(ax,,
)
,,
at x - x .... where subscripts x,,,+ and x,,, represent conditions at the interface on the two-phase and solid-phase sides, respectively. 3. N U M E R I C A L M E T H O D The theoretical formulation established in the preceding section requires a timeaccurate analysis. A dual-time-stepping numerical integration method is employed to circumvent the computational difficulties associated with the rapid transients during the ignition process. The scheme includes artificial time derivatives, so that the solution converged in pseudo-time corresponds to a time-accurate solution in physical time. The physical time step is chosen to be around one hundredth of the estimated ignition delay, or even less, to obtain reasonable temporal resolution. When marching from one physical time level to the next. all the conservation equations and associated boundary conditions are solved by treating the propellant surface temperature T~urand burning rate rb as the eigenvalues. The iteration starts with guessed T~ur and rb, which are bound by Eq. (30). The condensed- and gas-phase governing equations are solved with these guessed values and other boundary conditions. If the resulting temperature gradients do not satisfy the interracial energy balance equation, Eq. (29) is used to correct the values of Tsur and rb by means of a bisection method. The updated T~.r and r~, are then substituted into the governing equations for another solution of the temperature field. The iterative procedures are performed until Ts,,. and r~ converge, and Eq. (29) is satisfied. Finally, a solution at the physical time level is obtained when all the governing equations and associated boundary conditions are satisfied. In general, the gas-phase solver takes much more computational time than its counterpart for the condensed phase, due to the complexity of the chemical kinetics in the gas phase.
315 Calculations of chemically reacting flows often encounter numerical stiffness problems attributed to the wide variety of time and length scales associated with chemical reactions and transport processes. The problem can be effectively circumvented by using a combined Newton-iteration and (pseudo-) time-integration scheme originally developed by Kee et al. [77]. The Newton method works efficiently for linear systems but may fail to converge for nonlinear systems unless a reasonable initial guess is provided. Conversely, the (pseudo-) time-integration technique is more robust, but less efficient. To optimize the benefits of these two algorithms, computations usually start with the Newton method, and then switch to the time-integration scheme when the iteration fails to converge. After another trial solution is obtained with several time-marching steps, the Newton method is resumed to gain efficiency. The time step in the time-integration technique is sufficiently smaller than the physical time step in order to handle the numerical problems caused by the highly transient phenomena due to rapid chemical reactions. An adaptive-grid system is employed to further improve the convergence rate. A four-step Runge-Kutta method is used for temporal integration of the condensed-phase conservation equations, along with a second-order central differencing scheme for spatial discretization. Calculations start with an estimate of the temperature profile, obtained by solving an inert energy equation. The conservation equations of mass and species concentration are then integrated with the given temperature profile. The energy equation is subsequently solved with the newly obtained void-fraction and species concentration profiles to update the temperature profile. Since these equations are solved sequentially, iteration is required to get a converged solution. Once the temperature reaches the melting temperature, the movement of the solidliquid interface is determined from Eq. (31). The fixed-grid Eulerian method is employed for interface tracking. 4. DISCUSSION O F M O D E L R E S U L T S The theoretical model and numerical method outlined in the above sections were implemented to study steady-state combustion of nitramine monopropellants [33.34], laser-induced ignition of RDX [39,40], and steadystate combustion of nitramine/GAP pseudo-propellants [37-39]. The analyses were carried out over a broad range of operating conditions. Various important burning and ignition characteristics were investigated systematically, with emphasis placed on the detailed flame structure and the effect of the subsurface two-phase layer on propellant deflagration.
316 4.1. S t e a d y - S t a t e C o m b u s t i o n o f N i t r a m i n e P r o p e l l a n t s
Figure 7 shows predicted temperature distributions at several ambient pressures using the gas-phase chemical kinetics mechanism proposed by Yetter et al. [26]. The temperature increases monotonically from its initial value of 293K, and levels off at a value close to the prediction by the chemical equilibrium analysis. The final flame temperature increases with increasing pressure, whereas the flame-standoff distance exhibits an opposite trend owing to enhanced chemical-reaction rates at high pressures. No evidence is obtained of the existence of a temperature plateau in the dark zone regardless of pressure, which is consistent with the experimental observations of self-sustained combustion of RDX monopropellant [41 ]. It is worth noting that a dark-zone temperature plateau (at T 1500 K) was present in the laser-assisted combustion of RDX, while the existence of the dark zone was not evident in the self-assisted combustion. Liau and Yang [41] indicated that the chemical preparation and fluid transport time~, of the intermediate species produced in the primary flame must be comparable in order to form a dark zone.
3500
9
!
.
.
!
3000 v
.
"'"
.
!
'
9
-.
: 913 .
20 5
.
.
.
-
2500
~:1. 2000 1500 ooo
500
,
-o.o
ropellant surface 0.5
1.o
Distance a b o v e propellant surface, mm
Fig. 7 Temperature profiles of self-sustained RDX combustion at various pressures Figure 8 shows the burning rate as a function of pressure. Good agreement between predictions and measurements is obtained. A power law of the burning rate vs pressure is observed, rb = a p
n
(34)
where the pressure exponent n is about 0.83 (with p in atm), and the preexponential factor a equals to 0.3 cm/s for Ti = 293K. The increased burning
317 rate with pressure is attributed mainly to fast gas-phase exothermic reactions at high pressures and their influence on heat transfer to the condensed phase. 101
E O
.~
10~
- ~, 9 O 9
Prediction Zimmer-Gailer (1968) Glaskov (1974) Zenin (1995) _~
rr c cL _
o...
m
1
Tir~,w=293K 100
101 Pressure,
10 2
atm
Fig. 8 Effect of pressure on strand burning rate of RDX monopropellant; self-sustained combustion. The temperature sensitivity of burning rate defined in Eq. (35) is also examined, giving the result shown in Fig. 9.
=I(~r6)lr6~ I()(lnrb)~ P L-~ ~j~= ~ ~ The temperature sensitivity •p
(35) stays around
0.0028 K j for most cases. At
elevated pressures, the heat feedback from the gas phase to the condensed phase is higher, and thus the effect of initial temperature on the interfacial energy balance becomes less important. A numerical analysis on the temperature sensitivity for low-pressure conditions was further performed by Beckstead and co-workers [35]. The predicted temperature sensitivity was determined to be too low compared to the measurements, mostly due to the uncertainties associated with the treatment of the condensed phase in the model. A similar approach was applied to study the combustion characteristics of HMX monopropellant. A detailed description of the theoretical formulation and results is available in Ref. 37. Figure 10 shows the pressure sensitivity of the HMX burning rate. Good agreement was obtained with the experimental measurements by Zenin [11] and Atwood et al. [21]. The pressure exponent n in Eq. (34) was about 0.88, with the pre-exponential factor a equal to 0.35 for Ti = 293 K. The temperature sensitivity of burning rate defined by Eq. (35) at various pressures is shown in Fig. 11. There were noticeable discrepancies
318 between the measured and predicted values at pressures below' 20 atm, a phenomenon that may be attributed to the uncertainties in modeling the condensed-phase heat release process. More detailed understanding of the chemical kinetics in the condensed phase is required to improve model predictability, especially for low-pressure cases in which near-surface exothermic reactions play a more dominant role in determining propellant surface conditions than the heat feedback from the gas phase.
0.005
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . . . . . .
"7,
v, 0.0o4 . ...,,
.'~ dl
0.003
r
0.002 t,'l
E 0.001 100
..................... 101
102
Pressure, atm
Fig. 9. Temperature sensitivity of RDX burning rate; self-sustained combustion.
lOl~ -
'
. . . .
,,,I'
Exp.
(Atwood
'
'
. . . . . .
-~
,
. . . . .
02
E []
~
lOU
C
et al. [21 ])
,
i r e-
it_ / 10"21~u
..........
, 101 p, atm
,
Fig. 10 Pressure dependence of burning rate of HMX monopropellant; self-sustained combustion.
319 7 ~
%
, . . , , , , , ,
6
._r
5 4 t-
~ 0
'
9
9
9U ~
"1'
*
'
~
I
'
'
'
'
I
'
;
'
'
Exp. ( A t w o o d et al. [21]) Current Model
r
i
3
o,-,
.~-
2
.,,.,
~
r~
l 0 i-
1
,,
~
20
....
1
40
60
80
100
p. a t m
Fig.
1 1 Temperature
sensitivity
of buming
rate of HMX
monopropellant;
self-sustained
combustion.
In this chapter, the model results pertaining to the combustion-wave structure of RDX monopropellant are focused. A comprehensive description of theoretical formulation and results for combustion of HMX monopropellant can be found in Ref. 27. The calculated species-concentration profiles were validated against experimental data [22], which was obtained by means of a time-of-flight mass spectrometry technique at 0.5 atrn, as shown in Fig. 12. Good agreement was obtained except for the region next to the surface. The discrepancy may arise from the ambiguity in determining the location of the propellant surface in experiments. Due to the limitation of the spatial resolution (500 Bm), the diagnostic work defined the surface as the location where RDX was completely consumed. This analysis, however, predicted that an appreciable amount of RDX still existed at the surface since only limited RDX decomposition occurred in the subsurface region. If the spatial distribution of the calculated data was artificially shifted upward to the location where NO and HCN attained their peak values, then an improved agreement between the prediction and the measurement could be achieved. The species-concentration profiles revealed that the overall reaction mechanisms globally consist of three steps: (1) decomposition of RDX to CH20, HCN, NO2, etc. near the surface, (2) first-stage oxidization which includes formation of NO and H20 as well as removal of NO2, and (3) second-stage oxidization which includes conversion of HCN and NO to the final products such as CO, N2, and H2. It is worth noting that the highly exothermic reductions of HCN and NO usually occur at elevated temperature (T-- 2000 K) owing to the large activation energies required to initiate these reactions, which provide the major heat source for raising the
320
flame temperature to its final adiabatic value. The calculated molar fractions of the final product species are quite consistent with the chemical-equilibrium predictions, with the deviation being less than 2%.
Theoretical Calculation 0.40
. . . .
I
. . . .
I
. . . .
!
. . . .
I
. . . .
I
. . . .
1
. . . .
0.35 N2 0.30
.s
tT.
/ " ..... ~ . . . . . . . . / -
(i..;
0.25 0.20
."
~'./
/.,~..
~.;,
0.15
CO
/ ; : : " : ' " ".......... -
.4
i
(1)
_.
J
",,i.4....
.."
0.10 o " " "
~
%%"%'"... %
o S
"...
0.05 0.00 -0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Exp. Measurement (Korobeinichev, 1985) 0.40
....
, ....
, ....
, ....
, ....
, ....
, ....
0.35 r O 9. ~
0.30
t'zl "- 0 . 2 0 U.. "~
H20
o
---o
0.25
~'~'~~
0.15
/
:E
~~
0.10 0.05
~
r
Y~~('... 9
.,O ~ O "
"""
x .... x .... 0.00 . . . . -0.5 0.0 0.5
CO
x~.
'~~-,..... ...... NO HC,,~ - - ~ ...........~ ..............o .t . . . . 1.0
"-,,'."7":-9-=--,.._.._J. . . . . 1.5
2.0
2.5
3.0
Distance above propellant surface, mm Fig. 12 Distributions of major species concentrations of self-sustained combustion of RDX at 0.5 atm.
The combustion wave structure at 100 atm is shown in Figs. 13 and 14, exhibiting a close similarity to that at 1 atm except for the shorter flamestandoff distance (6 vs. 600 gin) and molten-layer thickness (2.1 vs. 66 l.tm).
321
The major difference lies in a smaller void fraction. The shorter molten-layer thickness and higher burning rate yield a shorter residence time for condensedphase reaction. Also. high pressure tends to retard the RDX evaporation, which dominates the gasification process in the two-phase layer. As evidenced by the large ratio of HCN to CH20 mole fraction, the endothermic decomposition, (R2), appears more profound at high-pressure conditions. This can be attributed to the higher surface temperature and heat transfer into the condensed phase.
3500
........
, .....
....,
....
, ....
, ....
f
3000 v
2500
d =
2000
l,.
4,,,*
p = 90 aim
4)
el. 1500
E
T i = 293 K rb = 12.0 mm/sec
10oo 500 !
,
,
,
-0.005
0.40
.
.
.
.
.
-0.000
.
.
.
0.35
.
.
I
.
.
.
.
0.005
.
I
.
1
.
.
.
.
0.010
.
.
.
I
9
I
.
.
.
0.015
9
-
9
I
.
.
.
!
.
,
.
0.020
.
.
1
.
.
.
1
t
,
.
0.025
.
.
!
.
.
,
0.030
.
.
RDX N2
g
0.25
"~. ........
/
LL 0 . 2 0 4)
I--HC~]
CO
,,,
o.15
!i//
0.10
0.05
j
0.00 -0.005
o I
"" '~i.
H2
~'..
~
... NO
7 .,2 ~ -0.000
0.005
..- :, . . . . O H , 0.010
0.015
0.020
0.025
0.030
Distance above propellantsurface, mm Fig. 13. Distributions of temperature and major species concentrations of self-sustained RDX combustion at 90 atm.
322
_ . . . .
,
. . . .
,
. . . .
..,
. . . . .
.
1.00
.~,j
700 p = 90 atm T i = 293
6O0
K
~
0.75
= o
L_
0.50
500 E
melting
~" 40o 300
point
F ~
. . . .
-0.004
,.
-0.003
'." 9 9 ,
-0.002
. . . .
",
-0.001
.....
0.25 0.00 -0.000
. . . . . . . . . . . . . . . . . . .
-0.005
1.00
Void
.L.''-
"'
0.20
",~
to o
X a n"
O
HCN :~ 4,,t -= 9 ., NOz,NO,H20 .._._~ / ]o.10 .~_r
u_ o
r
~ \Itit o.15 =u_
RDX
0.75
u. .'g_ o >
0.50
CH20,N20
0.25
0.00 9 -0.005
. . . . . . . . . . . . . . .
-0.004
-0.003
-0.002
.......
/ Y "~
Q.
r.n
\ I~/, 7 0.05 (D,_
~
.
-0.001
,~I 0.00 -0.000
Distance underneath propellant surface, mm Fig. 14. Close-up view of temperature and species-concentration profiles in subsurface region at 90 atm.
4.2. Laser-InducedIgnitionof RDXMonopropellant The entire laser-induced ignition process of RDX in an argon environment has been studied in detail [39,40]. Figure 15 shows the predicted temporal evolution of the temperature field at an incident laser heat flux of 400 W/cm 2 under atmospheric pressure. The initial temperature is 300 K. The interface between the subsurface and gas-phase regions is set to be x = 0, with negative and positive values of the x-coordinate representing the subsurface and gas phase, respectively. The surface temperature is rapidly increased to 475 K within 1 ms, due to the high intensity of laser heat flux. The profiles for t < 1
323
ms represent inert heating of the thin surface layer with conductive heat losses to both the solid- and gas-phase regions. The temperature rises in the gas phase at t = 2 ms are primarily caused by radiant energy absorption rather than exothermic reactions, because the extent of RDX decomposition in the gas phase is very limited at this stage of the event. At t = 2.9 ms, exothermic gasphase reactions start to occur, and a flame appears near the propellant surface at t = 3 ms. During the time period between 3 and 6 ms, the temperature continues to increase to around 1500 K, as a consequence of the heat release by exothermic reactions. As time further elapses, a luminous flame appears, and the temperature rises to its adiabatic temperature. The luminous flame is not stationary but regresses toward the surface. There is a time lag (about 4 ms) between the first appearances of the primary and secondary flames.
3500 3O00 ~-
,
:~ 2500 }-,s E
~
Propellant
'
7.25 ms
~ 7
ms
_
-~
L-- 2OO0I .~ 1500 1000 I 500 1 0.0
0.5
1.0
X, c m
Fig. 15 Evolution of temperature field during laser-induced ignition of RDX in argon at p = I a t m a n d Q~" = 4 0 0 W / c m 2.
Figure 16 shows a close-up view of the temperature evolution in the condensed phase near the propellant surface. The transient development of thermal-wave penetration into the subsurface region is clearly observed. The characteristic thickness of the thermal layer in the subsurface region is much thinner than that in the gas-phase region. Phase transition from solid to liquid can be indicated by the distinct change of temperature gradient at Tm = 478 K. Since most of the CO2 laser heat flux is absorbed by the thin surface layer due to the high absorption coefficient (2800 cm ~) of RDX at the wavelength of 10.6 ~tm, the formation of the mushy zone can be safely ignored. However, some propellants, including RDX, are quite transparent to plasma irradiation in the UV/visible wavelength range; thus, the appearance of the mushy zone may be
324 evident in that situation. Figure 17 shows the distributions of void fraction and species concentrations in the subsurface two-phase region when ignition is achieved at t = 7 ms. The extent of R D X decomposition in the condensed phase is very limited during the laser-induced ignition process up to 7 ms over the range of conditions studied, due to the short residence time and low temperature conditions. The molten layer in the subsurface region is not fully established within this time frame under atmospheric pressure. As indicated in the previous subsection, the steady-state combustion model predicts that the gas bubbles occupy about 45% of the volume at the surface under atmospheric pressure during self-sustained R D X combustion as a result of R D X evaporation and decomposition [34]. However, the surface void fraction during the selfsustained R D X combustion decreases significantly with increasing pressure [34]. 550 __
- "
i
- A m b i e n t Gas: A r ///J
500 d 450 m
6
~-400V
E
k
-~
4 ms
350 r
3~
': /
3 ms
-75
-50
9 ms
0
x. lam
Fig. 16 Close-up view of temperature evolution in subsurface region during laser-induced ignition of RDX at p = 1 atm and Q~,,, = 400 W/cm-'.
325 550
1.2L d
RDX x ! 000
1.01
~. 0.8~
Liquid Solid
j
1 500
~ 450 ._6
c > 0.6 =~ _
Meltin~ Point = 478 K
e--
400 ~ [..., HCN-~///
.~ 0 . 4 _
,~ 0.2~
t
~ Ambient Gas: Ar
0.0
e.,
CH.O.N.Oy
. . . .
i
-20
,
~
~o~
NO 2, N ~
,
i
,
,
,
9
- 15
i
- 10
. . . .
-5
350 0300
x, rtm
Fig. 17 Close-up view of temperature and species-concentration profiles in subsurface region at t = 7 ms (p = 1 atm and Qw~,= 400 W/cm2). The overall gaseous RDX ignition process can be divided into five distinct stages: thermal decomposition, first oxidation, chemical preparation, second oxidation, and completion stages. In stage I, RDX decomposes to lowmolecular weight species, such as CH20, N20, NO2, HCN, and HONO. This decomposition process is slightly endo-/exo-thermic or thermally neutral depending on the initial temperature. In stage II, oxidation reactions occur and release a significant amount of energy with the temperature reaching about 1500 K. The dominant net reactions in stage II can be given as follows. CH20 + NO2 => H20 + NO + CO HNO + HONO => H20 + 2NO 2HCN + NO2 => C2N2 + NO + H20 CO + NO2 => CO2 + NO 2HONO => NO + NO2 + H20 2NO2 => 2NO + 02
(-44 kcal/mol) (-23 kcal/mol) (-33 kcal/mol) (-53 kcal/mol) (8 kcal/mol) (29 kcal/mol)
(R4) (R5) (R6) (R7) (R8) (R9)
The heat release in stage II is mainly caused by the conversion of CH20 and NO2 to H20, NO, and CO, and to a lesser extent by the reactions of HCN and HONO. Stage III represents the chemical preparation time before the second oxidation reactions (stage IV) take place. The species formed in stage II are relatively stable, due to the high activation energies of their associated reactions, and require a finite time to oxidize further. The highly exothermic reactions occurring in stage IV may be attributed to the following net reactions.
326 2HCN + 2NO => 2CO + 2N~ + H, N~O + H~ => N~ + H~O C2N2 + 2NO => 2CO + 2N2 _
(-158 kcal/mol) (-78 kcal/mol) (-169 kcal/mol)
(R10) (R11) (R12)
The reduction of HCN and NO to N2, CO, H20, and H2 is largely responsible for the heat release in stage IV. Finally, all the final products are formed; no further reactions occur in stage V. Figures 18 - 23 show the temperature and species-concentration fields in the gas phase at various times. At t = 2 ms, the gas temperature increases by more than 300 K, although only a small fraction (less than 10 %) of the laser energy is absorbed in the gas phase. This is not surprising, because the heat capacity of the gas mixture is much lower than that of the condensed mixture. At t = 2.9 ms, small amounts of intermediate species, such as HCN, NO, HONO, CH20, N20. and NO2, result from thermal decomposition of RDX. The temperature rises to more than 800 K within 1 mm above the surface. Figure 10 shows the first appearance of the primary flame at t = 4 ms. The aforementioned RDX decomposition products, especially CH20 and NO2, undergo rapid reactions, which leads to the formation of NO, HCN, H20, CO, and N20 in the flame. The dominant net reactions in the primary flame zone can be given by (R4-R9). The temperature increases to about 1400 K. The species formed in the primary flame are relatively stable due to the high activation energies of their associated reactions, and require a finite time to oxidize further. At this stage, the fraction of laser absorption decreases significantly because of the rapid consumption of RDX. which is considered to be the only species absorbing a noticeable amount of laser energy in the gas phase. Figure 21 shows more details of the chemistry involved in the primary flame. The conversion of CH20, NO2, and HONO to NO, CO, HCN, etc. appears to be the major chemical mechanism releasing thermal energy. Figures 22 and 23 show the development of the secondary flame at t = 7 and 7.25 ms, respectively. The temperature increases from 1500 to 3000 K at this stage, and the heat release can be largely attributed to (R10R12). The conversion of HCN and NO to the final products seems to be the dominant net reaction in the secondary flame. Once the secondary flame appears, the intense energy release and heat transfer causes the flame to regress toward the propellant surface.
327
1.0 ~_ 0.9~-
800 t=2ms
o.8F 0.7 L
-'2 ~-u o.6 ~-
700 / ,
600
0.5 0.4
0.3F
500 E [.-,
,
400
0.2 0. I
RDX !
0.00
0.05
O. 10
O. 15
i
i
9
|
0.20
X, c m
Fig. 18 T e m p e r a t u r e a n d s p e c i e s - c o n c e n t r a t i o n p r o f i l e s in g a s p h a s e at t = 2 ms.
l.OF
"'
t i
0.8 ,- O.7 -?- 0.6
1000 900 800 :~
7oo
~
600
E
0.5 "-6 0.4 0.3
500 ~
0.2 400
O.l 0.00
0.05
0.10
0.15
0.20
X, c m
Fig. 19 T e m p e r a t u r e a n d s p e c i e s - c o n c e n t r a t i o n p r o f i l e s in g a s p h a s e at t = 2.9 m s .
328 2000
iOL 0.9~ 0.8 1 RDX 0.7
t=4ms
A
1750
/
1500~d
"~ 0.6 I
1250
0.5
!000 ~-
O.4 0.3 0.2 0.1
750 500
0.0
0.5 X, c m
Fig. 20 Temperature and species-concentration profiles in gas phase at t = 4 ms. 0.08 ~ E 0.07 ~
CH,O
CO
0.06 ~ N~O ~ ~ - ~ N 0.05 L HONO_ "-r u X _ ,~ NO, 0.04
F
. . . . . a 2000 t=4ms 1 1750
20
/// / / ) i \
1500 !250 ,~
co,.
I
0.02
750
0.01 ~
500
0.00
0.01
0.02
0.()3 0 . 0 4 0 . 0 5
0.06
0.07
x, cm
Fig. 21 Close-up view of temperature and species-concentration profiles in primary flame zone at t = 4 ms. A parametric study for investigating the effect of the absorption coefficient of vapor RDX on the overall ignition process has been performed by varying the absorption coefficient by 15 %. As shown in Fig. 18, the gas-phase temperature is rapidly increased by more than 300 K at t = 2 ms, with a small amount of the laser energy absorbed by the gas phase. At t = 2.9 ms, the gasphase temperature rises to more than 800 K, caused by the heat release from the exothermic decomposition reactions in the gas phase. After the inert heating, the heat release from the exothermic reactions becomes much more pronounced than the laser energy absorbed by the gas phase. Since only a small amount of the laser energy was absorbed by the gas phase, a change by 15 % in absorption
329 coefficient did~not influence, the inert heating time significantly. Overall, the effect of the absorption coefficient of vapor RDX on the CO2 laser-induced ignition was not noticeable over the parameter range studied herein.
1.0 !t 0.9
3500
t = 7 ms
0.8
3000
RDX
0.7 [-i
_,.~c'7--"
2500~:
".~ 0.6 0.5
2000 "~
0.4 0.3 0.2
1500 t--, ! 000
0. !
500
0.0
0.5
1.0
X, cm
Fig. 22 Temperature and species-concentration profiles in gas phase at t = 7 ms.
1.0 0.9
t = 7.25 ms
( ~
3500 3000
0.8 0.7
2500:~
"~ 0.6
2ooo .~
:~~~~ ! ~, 0.4
l ,
0.3
o e-
1500 '-
N, / CO
NO
,
0.2
OH
0,
A
-
\., ~------~---~
0.0
l
0.5 x, cm
',
.
.--7--"7_--
1000 500 1.0
Fig. 23 Temperature and species-concentration profiles in gas phase at t = 7.25 ms.
Figure 24 shows the evolution of the CN concentratiorL field. A noticeable amount of CN is observed at t > 7 ms. The concentrations of CN are usually small, except in the secondary flame, thereby serving as a good indication of the flame position. Parr and Hanson-Parr [23] conducted pioneering measurements of the transient flame structure of RDX using both UV-visible absorption and non-intrusive planar laser-induced fluorescence (PLIF). The experiments were
330
performed at three intensity levels of CO2 laser heat flux (i.e., 195,402, and 807 W/cm 2) under atmospheric pressure. Figure 25 shows the measured CN concentration profiles at various times for a laser flux of 402 W/cm 2. Comparison between Figs. 24 and 25 shows good agreement in terms of the CN concentration level. The measured ignition delay time (8.6 ms), however, is slightly longer than the predicted value (-- 7 ms), whereas the predicted flamestandoff distance, defined as the location of the peak value of CN concentration profile, is slightly longer than the measurement. 800 c _
,
700
7.25 ms / ! 7.15 ms
r,
," 600 500
i
C
._
400
I
I
E 300
, ..
,
I i
' :
-1
7 ms
i
-6 200 100 1 ,,.-
,
,A
0.0
1.0
0.5 X,
c m
Fig. 24 Predicted concentration profiles of C N at various times.
800 '
'
'
1
,
,
'
,
600
i !
700 9ms 20 ms 10ms ,/\ f~i
~ 5oo
~
8.6 ms
.2= 400 300 200
/
i i
100 0.00
0.25 X,
0
c m
Fig. 25 M e a s u r e d concentration profiles [23] of C N at various times.
Figure 26 shows the calculated and measured ignition delays of RDX induced by CO2 laser under atmospheric pressure. Excellent agreement is
331 achieved between the predicted and experimental data for laser intensities less than 200 W/cm 2. For 400 W/cm 2, the predicted ignition delay matches the measurements by Parr et al. [23] and Lee et al. [78]. However, the measured data of Vilyunov and Zarko [51] do not agree with the model prediction for laser intensities above 200 W/cm 2. Vilyunov and Zarko showed that the ignition delay increases with increasing laser intensity above 200 W/cm 2, whereas the results of the current model as well as Parr et al. [23] and Lee et al. [78] revealed the opposite trend. Vilyunov and Zarko [51] stated that the RDX ignition was controlled by the solid-phase kinetics at low laser intensities (below 200 W/cm2), whereas the gas-phase kinetics along with the liquid-phase decomposition governed the ignition process at high laser intensities. The current model, however, predicted that the gas-phase chemistry controlled the ignition process over the laser intensity range studied. Thus, the ignition delay became shorter at higher laser intensities, because the gasification rate at the propellant surface increased with increasing laser intensity. Vilyunov and Zarko [51] performed their experiment in both nitrogen and air under atmospheric pressure and /bund that the ignition delays were about the same within the measurement accuracy. Lee and Litzinger [78] utilized argon as an inert gas, whereas Parr and Hanson-Parr perform the experiment in air. The differences in ignition delay among these three sets of measured data, especially above 200 W/cm 2, can also be attributed to the variation in RDX sample preparation in each experiment. The RDX samples used by Parr and HansonParr [23] and Lee and Litzinger [78] were pressed military-grade RDX. Information about the samples used by Vilyunov and Zarko [51] was not available. ! 0 ~
~- I0~I t>
.,-
10.2
10.3
9 9 9 t> ,
Vilyunov and Zarko [51] Parr and Hanson-Parr [23] Lee and Litzinger [78] Current Model i
|
100
i
i
i
t> t~
I
l
i
I
|
, I ....
200 300 Laser Intensity (W/cm 2)
IlllJllllll,i
400 500600
Fig. 26 Effect of CO2 laser intensity on ignition delay of RDX monopropellant.
332 In the experiment by Parr and Hanson-Parr [23], a significant time lag was obtained between the first light and go/no-go times (about 85 -- 100 ms). First light was defined as the time when the luminous flame was first detected, whereas go/no-go was the time when a stable flame was achieved without the laser-assisted heating. The model predictions for the first light and go-no-go times, however, were about the same. In the experiments [23], the luminous flame progressed toward the surface immediately after the first light and moved away from the surface after the maximum temperature gradient was achieved near the surface. The model, however, did not predict this type of flame movement. The luminous flame continuously progressed toward the surface until steady-state deflagration was achieved. The discrepancy between model predictions and experimental observations may be attributed to the heat loss to the ambience. The entire ignition process was treated as adiabatic in the model, whereas heat losses from both the gas-phase flame and the condensed-phase region to the surrounding might be significant in the experiments, in which continuous laser heating was required in order to achieve self-sustained combustion by fully establishing the condensed flame. This suggests that during the ignition stage, heat loss in the condensed phase was too rapid compared tO the heat transfer from the gas-phase flame to the surface. The discrepancies among the existing experimental results may be attributed to the uncertainties associated with measurements under different types of experimental conditions. It is clearly evident that more measured data is needed for model validation. Nonetheless, the present model provides detailed insight into the key physiochemical processes involved in the laserinduced ignition of RDX, and can be effectively used to estimate ignition delay, heat release mechanisms, and flame structure.
4.3. Steady-State Combustion of HMX/GAP and RDX/GAP PseudoPropellants Recently, Yang and co-workers performed numerical analyses to investigate the combustion characteristics of HMX/GAP and RDX/GAP pseudopropellants over a broad range of pressure and laser intensity with various compositions [37-39]. Summaries of the model results for both HMX/GAP and RDX/GAP are given below. 4.3.1 HMX/GAP Pseudo-Propellant Figure 27 shows the temperature and species-concentration profiles in the gas phase during HMX/GAP pseudo-propellant combustion at a CO2 laser intensity of 100 W/cm 2 under atmospheric pressure. The ratio of HMX to GAP mass fraction is 8:2. Reasonable agreement was achieved with the experimental data reported in Ref. 3. The temperature rises rapidly from 677 K at the surface,
333 levels off around 1200-1600 K, and further increases to its final value at 2780 K. The flame can be divided into three regions: 1) the primary flame, 2) the dark zone, and 3) the secondary flame. The dark zone is a nonluminous region between the primary and the secondary flame, and is characterized with a temperature plateau. The concentrations of HCN, NO, and H20 in the dark zone appeared to be similar to those of pure nitramine propellants [3]. The rapid conversion of HCN and NO to N2 and CO in the secondary flame zone were successfully predicted. The dominant net reactions in this stage are as follows. 0.35
3000
0.30
It, CO
g
0.25 - HCN 9~" ~ ~"H O ~0.20 - NO :
~ ~
l
~
~
][]
~
l
- 2500 i2000 v~. 1500
~0.15 ~ ~----" = ~------2~0"0.L___._N.-" _ _ - - ~ J ~
~C
H'O H/CN.N,O
o f~tqfl" .... 0
1 1000 ~
co: ],oo co,
\ ~-I
No
. , , 1~ . . . . " 2, . . . . 3~k~.-g--. . . . . 4. . Distance above Propellant Surface, nun
50
(a)
0.40 I0.30
. .HCN . . . . . . . .
'N2 '
'
'
:
.~_ ~o
0.20
NO
H.O
O
0.10
0"000
-
-
,i Distance above Propellant Surface, turn -
2
6
(b) Fig.27 (a) Calculated and (b) measured [3] species-concentration profiles of gas-phase flame of HMX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity of 100 W/cm2. 2HCN + 2NO => 2CO + 2Nz + Hz NzO + H2 ==>Nz + H20
(R13) (R14)
334 C2N2 + 2NO ~ 2CO + 2N2
(R15)
These reactions are highly exothermic and usually take place at high temperatures due to their large activation energies. The predicted flame standoff distance of 3 mm is slightly shorter than the measured value of 4 mm, partly because of the ambiguity in defining the propellant surface during experiments. Figure 28 shows a close-up view of the primary flame immediately above the propellant surface, which extends over a length of 100 ~tm. The dominant reactions in this oxidation stage are R16. R17, and R3. HMX ~ 4CH20 + 4N20 HMX ~ 4HCN + 2(NO2 + NO + H20)
(R16) (R17)
The prediction of N20 concentration was satisfactory compared with the measurement [3]" however, NO2 and CH20 appear to be consumed too fast. Intermediate reactions forming CH20 and NO2 are still lacking in the nearsurface region in order to yield better agreement with experimental results. Conversion of GAP and GAP ~ to N2, HCN, CO, NH3, CH20, CH3CHO, H20, C2H3CHO, C2H4, CH3CHNH, and CH2CHCHNH occurs in a very short distance (---10 btm). The GAP decomposition is a highly exothermic process releasing a significant amount of energy in the gas phase. However, at the same time, the heat feedback from the gas phase to the surface is reduced due to the dilution of reactive species by the GAP pyrolysis gases. The decomposed fuel fragments, such as CH2CHO, C2H3CHO, CH~CHNH, and CH2CHCHNH. further react to form CH3, HCO, C2H3, and HeCN.
~
1500
H C ~ o =
U
HMX
0.2
1200
/ ;"~,O""~
L
- oo
~0. I
_
~_. . . . . . . . . . I )~
~
,5
-z---z- -
~
7 77;Z~-
10 ~
'
. _~-~-Z,._Z>~. -_ 10 ~
~ .
~ ,
, 7,,
~co: -~-~ 1
0:
-03
Distance abovePropellantSurface,lam Fig. 28 Temperature and species-concentration profiles in near-surface region of HMX/GAP pseudo propellant (mass ratio 8:2) combustion at 1 atm and laser intensity 100 W/cm2.
335
The species-concentration and temperature profiles in the foam layer are shown in Fig. 29. An appreciable amount of HMX evaporates to form gas bubbles in this region, but the extent of decomposition through the pathways (R1) and (R2) appears to be limited. On the other hand, most of the GAP compound is consumed to become GAP* and N2, releasing heat to support pyrolysis in the condensed phase. Further decomposition of GAP* according to (R4), however, is constrained due to the low temperature condition. The predicted surface temperature and foam-layer thickness are 677 K and 30 gm, respectively. 0.5
800 r
HMX, u/2
= 0.4'
750
"z 0.3 ~
:~
"~ .q ~ 0.2
~
0
700
-3
GAP,,, 650
:r.
0.1 ~
600
-30
-20
-10
0
Distance underneath Propellant Surface. gm Fig. 29 Temperature and species-concentration profiles in subsurface of H M X / G A P pseudo propellant (mass ratio 8:2) combustion at 1 atm and laser intensity of 100 W / c m 2.
Figure 30 presents the corresponding temperature sensitivity of burning rate. which appears to be independent of pressure and has a value twice greater than that of pure HMX. In general, the effect of preconditioned temperature on propellant burning rate diminishes with increasing pressure and impressed laser intensity. The enhanced heat transfer to the propellant surface due to large energy release and reduced flame standoff distance in the gas phase at elevated pressure overrides the influence of preconditioned temperature in determining the energy balance at the surface, and consequently decreases the temperature sensitivity of burning rate. Figure 31 shows the effect of propellant composition on burning rate at various pressures. The burning rate in general decreases with the addition of GAP. which releases a substantial amount of N2 through the C-N3 bond breaking in the near-surface region. Although the process is exothermic, the pressure of N2 and large fuel fragments dilute the concentrations of surface
336
reactive species, and consequently reduces the rate of energy release from HMX reactions. The heat feedback to the surface decreases accordingly, rendering a lower burning rate. Another factor contributing to this phenomenon is the blowing effect of the GAP compound, which tends to push the primary flame away from the surface. The situation is. however, different at high pressures. The burning rate of HMX/GAP pseudo-propellant with a mass ratio of 9"1 is greater than that of pure HMX for p > 30 atm. i
T
">
4
~
3;-
No Laser Heatin~
F
',-=
>, - r ._ ._ ....,
.~
1 -1 4
o
,o p,
Fig. 30 Temperature 8:2); self-sustained
sensitivity
of burning
80
00
a r m
rate of HMX/GAP
pseudo
propellant
(mass
ratio
combustion.
9
,
,
,
,
,
,
r , !
.
.
.
.
.
,
10 ~ ~.
,
, ] ,, , ,
~
No Laser Heatin~
~ r ~ ~
i.
_,z-
/
~
"
9:1
~ ~ L
10 t;
-I
10:0
/ --
ic~-2
/
~
8:2 73
- ..... l
i
L
,
,
i
i
i
I
10 ~ p, atm
~
~
,
,
,
I 10
I 2
Fig. 31 Effect of propellant composition on burning rate at various pressures; self-sustained combustion. Figures 32 and 33 show the effect of laser intensity on burning rate for several mixture ratios at 10 and 100 atm, respectively. At 10 atm, the burning
337
rate increases with increasing CO2 laser intensity. Although GAP decomposition is highly exothermic, the burning rate decreases with increasing GAP concentration since the fuel-rich pyrolysis products of GAP reduce the flame temperature and move the flame away from the surface. At a high pressure of 100 atm. the intensive heat transfer from the flame to the surface overrides the effect of surface radiant energy absorption. The burning rate thus appears to be insensitive to the impressed laser intensity. The influence of GAP concentration on burning rate exhibits a different trend from that at 10 atm due to the variation of surface temperature, a phenomenon that has been elaborated in connection with the discussion of Fio 31 0.40
[:
. . . . .
,
. . . .
,
. . . .
,
. . . .
,
,
p = !0 atm
0.35 ~
1o-
)_ t..
0.30 ~
~
- - -'~
E 0.25 L-
......
0.20
.. . . . . . . .
_ .........
-~
"~ 0.15 ?-_-
"~
0.I0
E~_
0.05
~
Mass Ratio (HMX:GAP)
....
0.00
I . 1O0
. . .
I
. . . .
9 ,
lo:o 9:1
v ....
8:2
i
-l
. . . .
! 50 200 250 Radiant Energy Flux, W/cm-"
F i g . 32 E f f e c t o f p r o p e l l a n t c o m p o s i t i o n p = 10 a t m .
3.50~
I
o A
I
,
300
o n b u r n i n g r a t e at v a r i o u s C O 2 l a s e r i n t e n s i t i e s ;
. . . . . . . . . . . . . . . . . . . . .
3.25 E- p = 100 atm
Mass Ratio (HMX:GAP)
r-
3.0OE
o a
10:0 9:!
.... * ....
8:2
-
"~ 2.75 ~
-
-~
~" 2.50 E-
-~
~: 2.25 ~ " ~
~ ............
..........
0-- . . . . . . . . . . . . . .
-,i
1.75 ~-
1.50E!.25 ~r
1.00r
-
~ . . . . 100
, . . . . 150 Radiant
F i g . 33 E f f e c t o f p r o p e l l a n t c o m p o s i t i o n p = 100 a t m .
, 200
Energy
. . . . Flux,
on buming
, 250
. . . .
J 300
,~
Wlcm"
r a t e at v a r i o u s C O 2 l a s e r i n t e n s i t i e s ;
338
The effects of laser heat flux and pressure on the burning rate of H M X / G A P pseudo-propellant (mass ratio 8"2) are shown in Fig. 34. The impressed laser flux causes a substantial increase in burning rate at low pressures (e.g., 1 and 10 atm). The effect, however, diminishes at high pressure, since the heat feedback from the gas phase overshadows the surface laser absorption in determining the energy balance at the surface, as shown in Fig. 35. The heat transfer to the burning surface increases almost linearly with pressure. Figure 36 shows the propellant surface temperature as a function of radiant heat flux at several pressures. The trend resembles that for the burning rate shown in Fig. 34. l
i
-
,
:
,
,
i
,
~
9
:
-
-
----1
p = 1 0 0 atrn o
O
1 .+
.-p
=
10
atrn +
"
p
100
=
I
atm
150 200 250 Radiant Energy Flux, W/cm2
300
Fig. 34 Effect of pressure on burning rate at various CO2 laser intensities (HMX/GAP mass ratio 8:2). 10~F----~
!~
p
=
i00 atm
0
-+. -+
9
,,
"= 103 ~ 39 _p -
.~
=
10 a t m
-~
_
10-~p =
I atm
_~
U_.,
92 .
C
10 j '
10 ~)L
,
~
100
. . . . .
,
,
:
.
~
. . . .
,
. . . .
150 200 250 Radiant Energy Flux, W/cm"
,
300
,
Fig. 35 Heat feedback to propellant surface at various CO2 laser intensities and pressures (HMX/GAP mass ratio 8:2).
339
The melt-layer thickness and surface void fraction are shown in Figs. 37 and 38. respectively. They both decrease with increasing radiant heat flux at low pressure, but remain almost fixed at high pressure. It should be noted that the bubble formation rate can be enhanced with increasing temperature, but may also be reduced by the decreased residence time resulting from the increased burning rate at high temperature. The present case shows a net decrease in the surface void fraction with increasing pressure.
850 F 825 ?,s 800 i :~ ~ 775
p = 100 atm
O
o
.O
750 .'-3
p = 10 atm
"" 725 ~2-- 700 ~_
p = ! atm
675 ~650
-~
~
~ .
. . 1O0
.
. 150
200
250
300
Radiant Energy Flux, W/cm 2
Fig. 36 E f f e c t o f C O 2 laser i n t e n s i t y on s u r f a c e t e m p e r a t u r e at v a r i o u s p r e s s u r e s ( H M X / G A P m a s s ratio 8:2).
It'~lU2 ~
1
'
E•.•.•tm ~-
L !
o_____.____.p= 10atm
~= 101
t-
i
1-
I
p = 100 atm
0
l 0~ [ ' ,
1O0
.
.
.
.
t
150
;
0
~
i
a
I
200
0
i
m
A
i
I
250 Radiant Energy Flux, W/cm-"
~
a
i
,
!
,
300
Fig 37 E f f e c t o f C O 2 laser i n t e n s i t y on m e l t - l a y e r t h i c k n e s s at v a r i o u s p r e s s u r e s ( H M X / G A P m a s s ratio 8:2).
340 10 ~ C
-
_
I
,
'
~
'
"
I
'
-
*
'
I
:
"
,
9
I
'
'
'
'
i
'
p = I atm
-I
.,
p = 10 atm (>
r-
=
L !
p =
o
100 atm o
o
t_
i
| &in--'t 1,j
-
,
100
. . . .
I
150
~
.
J
,
I
200
:
,
,
I
250
,
.
,
,
~
,
300
Radiant Energy Flux, W/cm:
Fig. 38 Effect of CO2 laser intensity on surface void fraction at various pressures (HMX/GAP mass ratio 8:2). 4.3.2 RDX/GAP Pseudo-Propellant In general, the results from the RDX/GAP combustion model described in Ref. 38 show good agreement with the measured burning rates at atmospheric pressure. The measured burning rate of RDX/GAP pseudo propellant with a mass ratio 8:2 was 0.8 mrn/s at 1 atm with a CO2 heat flux of 100 W/cm 2. The calculated value at the same condition was 0.88 mm/s. At 300 W/cm 2, the measured and predicted burning rates were 1.9 and 2.18 mm/s, respectively. The flame structure observed in experiments using TQMS [3] was also reasonably well predicted by the model. Figure 39 shows the predicted and measured [3] species concentration profiles in the gas phase at 1 atm and 100 W/cm 2. Similar to the HMX/GAP combustion, it is found that HCN, NO, and H20 are the major intermediate products in the dark zone. The conversion of HCN and NO to N2 and CO dominates the luminous flame while the consumption of formaldehyde, NO_,, and N20 accounts for the primary flame above the surface. In contrast to RDX combustion, a noticeable amount (1-2%) of CH3CHO was observed near the surface. Here, the agreements between the predicted and measured concentration profiles of CO, CO2, and formaldehyde are not as good as the others. Chemical equilibrium calculation was also performed. This calculation result matches the model output but not the experimental data. Even though the agreement between measured and computed burning rates is reasonably good, further investigations into the combustion wave are suggested to resolve the discrepancy in flame structure.
341 0.4
r--
.o....
C
0.3 ~-
HeN NO
u_
o
H20
0.2
.(1)
c.~ oo
/ ~
N.,O
o.1
00
1
2
3
H O
4
5
x, m m
(a)
0 . 4 r-
=
o_
~
N2
0.a i
;
t.u
0.2 " oo
.o_ L~
Q.. (.f)
0.1
0~
~
.
.
.
.
1
.
.
.
.
.
.
2
.
.
.
.
.
.
.
3
.
4
x, m m
(b) Fig. 39 (a) Calculated and (b) measured [3] species profiles of the gas-phase flame of RDX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W/cm'-. In the foam layer, Fig. 40 shows that the predicted temperature rises from the melt point of RDX at 478 K to around 590 K at the propellant surface. The mass traction of liquid RDX originates at 0.8 and decreases slightly mostly through evaporation and partially through decomposition. The void fraction increases from 0 to almost 9 % due to the formation of bubbles containing vapor RDX and a small amount of decomposed gases. Consistent with the condensed-phase kinetics, the extent of GAP decomposition is negligible at temperatures lower than 600 K. The mass fraction of GAP remains at 0.2 throughout the loam layer, and then evolves into the gas phase. Figure 41 shows the predicted temperature, void fraction, and condensed species
342 concentration profiles in the region immediately above the propellant surface. GAP starts to decompose in the gas phase when the temperature reaches 700 K. At this stage, GAP x is immediately formed due to the elimination of N2 and reaches its maximum concentration within a short distance (less than 0.004 cm). The peak value of GAP" mass traction is less than 10%. The calculated concentration of carbon residue in this case is negligible. If the propellant surface is defined as the location where all condensed species are gasified, the surface temperature would be around 1000 K, consistent with GAP combustion. o.1
6OO
0.09 580
t-
R
E v
0.08 i!
0.07 32
560
0.05
o > "t2 ~-
0.04
co u3
0.06 .,w 540 --
i
O.
E
t.._o
520
o// GAP,/10
~0.03
~ 0 02
/)/
01 -20
-15
9
~
~ CD
~o
X, p m
Fig. 40 Predicted flame structure in the foam layer of RDX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W/cm 2.
1500
1, co .,_, ~_,
Void Fraction
0.8
.
~
~
IJ_ f,~
120O ,,e"
(f) t~
0.6~-
ffl .~ o
0.4
03 0
T
_
~ c~
900 E !_
FGAP ~.
0.2.
0 >
600 _
ol
. . . .
~ -
~
~._.
-.s~, . .
10
x, pm
Fig. 41 Predicted temperature, void fraction, and condensed species concentration profiles in the near surface region of RDX/GAP pseudo propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W/cm2.
343
Figure 42 shows the predicted pressure dependence of burning rate for a RDX/GAP pseudo-propellant with a mass ratio of 8:2. It is found that the burning rate-pressure relation follows a power law which is applicable to many propellants with the exponent n = 1, whereas n = 0.83 for pure R D X . The
exponent value n = 1 indicates that the addition of GAP does alter the combustion characteristics of RDX. Figure 43 shows the temperature sensitivity defined in Eq. (35) of burning rate at various pressures. The temperature sensitivity of burning rate decays at high pressures since the heat feedback is more profound than the effect of initial temperature on the burning rate.
3f~_:: T , = 2 9 3 K '
'
....
~ .... . . ~'"'~{
/
r
[ !
c -~ 133
/ "
0.1
.-
..o.. C r b = a pn a = 0.02 cm/s n=l
. p" /
/
/
/
/
o3
'
lb
'
'2's
....
s'o"~'i'ir 100
p, atm
Fig. 42 Predicted pressure dependence of burning rate of RDX/GAP pseudo propellant (mass ratio 8:2). 0.005
. . . . . . . . . . .
T,, ,
L
,,,,e.
0.00a++ 9, . . 7
t
.~_ ~-
f \'\
\
,.-'~0.003 1 0 >, 0.002
~
s162 o.ool
" \ \ \.
I
o~
'
k ....... " O ~ ' ~ - ~ . ~ . B ......
1'o
'
'2's
. . . . .
....
B.--
5'o'"~'+'ioo
p, atm
Fig. 43 Predicted temperature sensitivity of burning rate of RDX/GAP pseudo propellant (mass ratio 8:2).
344 Similar to results of the HMX/GAP analysis, the combustion characteristics of RDX/GAP pseudo-propellant at various pressures and initial temperatures were investigated [38]. The surface temperature increases linearly with increasing pressure on the logarithmic scale, but it is not very sensitive to the initial temperature. This is understandable because the surface temperature is resolved by an energy balance, and the heat flux is strongly dependant on the pressure but not the initial temperature. The adiabatic flame temperature increases with both increasing pressure and initial temperature. The increase is not linear due to the limitation of grid resolution and the non-linearity of chemical kinetics. The melt-layer thickness decreases with increasing pressure but is not sensitive to the initial temperature. In general, the melt-layer thickness decreases with increasing burning rate, but increases with the higher values of thermal conductivity of the propellant. As shown in Fig. 42, the burning rate is linearly dependant on pressure, and thus the pressure dependence of melt-layer thickness is also linear. The initial temperature of propellant does not exhibit a strong effect on the melt-layer thickness, because both the burning rate and thermal conductivity are not very sensitive to the initial temperature. The surface void fraction decreases with increasing pressure, but increases with increasing initial temperature. It is not surprising because the bubble formation strongly depends on the evaporation process, which is retarded at high pressures but enhanced at high initial temperatures. The effects of laser heat flux on the burning rate. surface heat flux, surface temperature, melt-layer thickness, and surface void fraction at pressure levels of 1, 10, and 100 atm were numerically investigated. The burning rate and surface temperature increase with increasing laser heat flux. The effect decays with increasing pressure because the heat feedback from the gas phase increases with increasing pressure. The melt-layer thickness exhibits an opposite trend; it decreases with increasing burning rate, and its decreasing rate is consistent with the increasing rate of burning rate. In contrast to the heat feedback from the gas phase at high pressures, the laser heat flux increases bubble formation, up to 50% at the surface at 1 atm and 300 W/cm 2. The final set of results show the effects of binder mass fraction on combustion characteristics over a broad range of pressure and initial temperature. Here, it is possible to utilize the model to describe experimental observations. For example, the burning rate of pure GAP is higher than that of HMX, but the addition of GAP into HMX lowers the burning rate [24]. In contrast, recent measurements [3] show the enhancement of burning rate by adding GAP into RDX or HMX. Both observations have been reproduced by the model. Figure 44 shows the effects of initial composition and pressure on the burning rate of RDX/GAP pseudo propellants. The burning rate decreases in the case of higher GAP composition because GAP decomposition produces
345
inert gases that dilute the concentrations of surface reactive species, and thus retard the heat feedback from the gas phase, as shown in Fig. 45.
o~
9
'
~- M a s s
ratio (RDX:GAP)
'
------10:0 - . . . . ........
9 10'; --
,
,
, ,
1 , I
,
'
'
'
'
'
"1
'.~1 . / ~
~.~
9:1 8:2
rr 9-c-
10'
rn no laser !
'
10 5
.
. . . . . . . . 1 0. ' 0
.
.
.
.
i
10 2
p, a t m
Fig. 44 Predicted effect o f propellant f o r m u l a t i o n on burning rate at various pressures.
104
. . . . . . . .
~- M a s s ~
.~
- - - . . . . . .........
103.
,
. . . . . . . .
ratio (RDX:GAP)
.............
' '".~
10:0
9:1 8:2 7:3
- " t-"~..--
"
-
ii
37. 102 / / /
/ /
J
/
/
no laser i .
.
.
.
,
~
02
p, a t m
Fig. 45 Calculated gas-phase heat feedback to propellant surface at various composition and pressure levels. It is evident that the heat feedback is a controlling factor for the burning rate in all the cases without laser, because the pressure dependence of burning rate follows the same trend as that of heat feedback. The addition of GAP modifies the slopes (pressure dependencies) in Figs. 44 and 45, but not in a consistent manner. A small amount of GAP (10% by weight) increases the slope and makes the system unstable, while more GAP (30% by weight) restores the slope to the pure RDX case but reduces the burning rate by more than 50%. Figure
346 46 shows the burning rates at l0 atm with various compositions and laser levels. The profiles of mass ratios 10:0 and 9:1 are very close, indicating the burningrate change due to the addition of a small amount of GAP is negligible for laser heat fluxes ranging from 100 to 300 W/cm=. For higher GAP compositions (20 and 30 % by weight), the burning rates decrease at 100 W/cm 2, but increase at 200 and 300 W/cm z. The effect is more profound at low pressures since the conductive heat feedback from the gas phase is of less importance in the case of laser-assisted combustion. More experimental data, however, is required for model validation as well as an improved chemical kinetics mechanism of GAP decomposition. ~'"'~"' .'_ ~ A t ~
' .... p = 10 atm
~ ....
~ ....
'
....
~
'
0.40 t-
-I
i ""
E 0.35_ . ~ 0.30 ~n"
.
. ~ . ~ . ~ - /
v---
.~
/ /
cL_
0 . 2 0 - --
-~
.~.g2- .........
_
c- 0.25 2-
./
--
M a s s Ratio ( R D X : G A P ) ,,- I o
~r "
10:0 -3 9:1
--a--
0.15 0.10:'
.
.... "
~
~ ' 100
.
I
150 Radiant
.
.
,
,
E
200
Energy
,
,
- ~ - -
8:2
~--
7:3
1
.
.
.
250
.
1
-t
~
51
300
Flux, W/cm 2
Fig. 46 Predicted effect of propellant formulation on burning rate at various laser and composition levels.
CONCLUDING REMARKS Comprehensive analyses have been developed and performed to investigate the steady-state combustion and transient ignition behavior of nitramine monopropellants and nitramine/GAP pseudo-propellants. The combustionwave structures of these propellants were numerically studied over a wide range of operating conditions. These models accommodate detailed chemical kinetics and transport phenomena in the gas phase, and thermal decomposition and phase transition in the condensed phase. Parametric studies were carried out to investigate the propellant burning characteristics and chemical pathways, with special attention given to the effects of the subsurface two-phase region on the flame behavior. In general, good agreement between the measured and predicted burning rates as well as their temperature and pressure sensitivities was achieved. The calculated species profiles matched reasonably well with the measurements. The steady-state combustion model was extended to simulate
347 the entire laser-induced ignition process of RDX monopropellant. Emphasis was placed on the ignition delay and key physiochemical processes responsible for achieving ignition. The predicted ignition delay shows good agreement with experimental data. The propellant gasification rate increases with increasing laser intensity, which in turn gives rise to a shorter ignition delay. In spite of the accomplishments achieved so far, several challenges remains to be circumvented. One major difficulty in both experimental and theoretical investigations lies in the treatment of the two-phase near-surface region, which includes an array of intricacies such as thermal decomposition, subsequent reactions, evaporation, bubble formation and interaction, and interfacial transport of mass and energy between the gas and condensed phases. Nonetheless, the existing models provide a solid basis for investigating various underlying processes involved in the combustion and ignition of energetic materials. ACKNOWLEDGEMENTS This work was supported partly by the Pennsylvania State University, partly by the Army Research Office under Contract DAAL 03-92-G-0118, and partly by the California Institute of Technology Multidisciplinary University Research Initiative under ONR Grant No. N00014-95-1-1338. The authors are indebted to Dr. Yeong Cherng (John) Liau for his contributions in developing the RDX ignition and combustion models.
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